Tootfinder

ASD, emotional memory, fears
Emotional memory is a bitch, and people in the spectrum are particularly vulnerable to it.
Let's say that something triggers the emotion of fear in you. You may be consciously recalling some bad memories, you may be imagining a possible outcome. However, when emotional memory comes into action, things are much worse. Your nervous system immediately brings the deep feeling of fear that is associated with the memory. You may even no longer be able to recall the memory, forget it entirely, yet your mind will ceaselessly keep hitting you with a whole set of emotions that you can't control, every single time it happens.
What's even worse, these things add up. Bad memories create fear. Fear creates more bad memories. These memories amplify the emotional reaction — and the wheel turns.
But the worst is the lack of understanding. People telling you that you are being irrational, that you are being an embarrassment to your family, that they have to give stuff up because of you. So the emotional memory becomes richer with the feelings of embarrassment, guilt and low self-esteem. All coalescing into a huge ball of emotion.
Today, you know it's not true. The fear wasn't irrational at all, it's pretty understandable in people who are #ActuallyAutistic, even "typical". Yet, what's the point of knowing that, if these emotions are deeply seated in your memory, and they will haunt you forever, and prevent you from ever having an illusion of normal life?

This https://arxiv.org/abs/2302.03923 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Uniform Diophantine approximation with restricted denominators
Let $b\geq2$ be an integer and $A=(a_{n})_{n=1}^{\infty}$ be a strictly increasing subsequence of positive integers with $η:=\limsup\limits_{n\to\infty}\frac{a_{n+1}}{a_{n}}<+\infty$. For each irrational real number $ξ$, we denote by $\hat{v}_{b,A}(ξ)$ the supremum of the real numbers $\hat{v}$ for which, for every sufficiently large integer $N$, the equation $\|b^{a_n}ξ\|<(b^{a_N})^{-\hat{v}}$ has a solution $n$ with $1\leq n\leq N$. For every $\hat{v}\in[0,η]$, let $\hat{\mathc…

This https://arxiv.org/abs/2309.12213 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The Sigma invariants for the Golden Mean Thompson group
We use a method of Bieri, Geoghegan and Kochloukova to calculate the BNSR-invariants for the irrational slope Thompson's group $F_τ$. To do so we establish conditions under which the Sigma invariants coincide with those of a subgroup of finite index, addressing a problem posed by Strebel.

In nem Buch drüber gestolpert und gefiel mir in der Formulierung "A nudge alters the choice situation to avoid triggering heuristics that lead to irrational behavior."

Irrational-window-filter projection method and application to quasiperiodic Schr\"odinger eigenproblems
Kai Jiang, Xueyang Li, Yao Ma, Juan Zhang, Qi Zhou
https://arxiv.org/abs/2404.04507

Irrational-window-filter projection method and application to quasiperiodic Schrödinger eigenproblems
In this paper, we propose a new algorithm, the irrational-window-filter projection method (IWFPM), for solving arbitrary dimensional global quasiperiodic systems. Based on the projection method, IWFPM further utilizes the concentrated distribution of Fourier coefficients to filter out relevant spectral points using an irrational window. Moreover, a corresponding index-shift transform is designed to make the Fast Fourier Transform available. The corresponding error analysis on the function appro…

In her opening keynote at KubeCon CloudNativeCon Europe in Paris, Priyanka Sharma, executive director of the Cloud Native Computing Foundation (CNCF), spoke of AI being in an "irrational exhuberance" phase, meaning that expectations are moving well ahead of delivery.
https://www.

Harnessing the 'irrational exhuberance' around AI - CNCF's Priyanka Sharma
In her opening keynote at KubeCon + CloudNativeCon Europe in Paris, Priyanka Sharma, executive director of the Cloud Native Computing Foundation (CNCF), spoke of AI being in an "irrational exhuberance" phase, meaning that expectations are moving well ahead of delivery.

This https://arxiv.org/abs/2404.00508 has been replaced.
link: https://scholar.google.com/scholar?q=a

Tiling spaces are covering spaces over irrational tori
We study tiling spaces in the diffeological context. We prove some basic diffeological properties for tiling spaces and analyze two different fiber bundle structures of one-dimensional tiling spaces over the irrational torus. We use the diffeological classification of irrationatl tori which captures their arithmetical escence in order to inherit the diffeological equivalence in the context of tiling spaces.

MAGA Republicans to a tee.
"Paranoid thoughts can become delusions when irrational thoughts and beliefs become so fixed that nothing can convince a person that what they think or feel is not true."
:mastodon:
https://mhanational.org/conditions/par

Irrational rotations and 2-filling rays
Lvzhou Chen, Alexander J. Rasmussen
https://arxiv.org/abs/2403.00097 https://arxiv.org/pdf/24…

Irrational rotations and 2-filling rays
We study a skew product transformation associated to an irrational rotation of the circle [0,1]/~. This skew product keeps track of the number of times an orbit of the rotation lands in the two complementary intervals of {0,1/2} in the circle. We show that under certain conditions on the continued fraction expansion of the irrational number defining the rotation, the skew product transformation has certain dense orbits. This is in spite of the presence of numerous non-dense orbits. We use this …

Irrational-window-filter projection method and application to quasiperiodic Schr\"odinger eigenproblems
Kai Jiang, Xueyang Li, Yao Ma, Juan Zhang, Qi Zhou
https://arxiv.org/abs/2404.04507

Irrational-window-filter projection method and application to quasiperiodic Schrödinger eigenproblems
In this paper, we propose a new algorithm, the irrational-window-filter projection method (IWFPM), for solving arbitrary dimensional global quasiperiodic systems. Based on the projection method, IWFPM further utilizes the concentrated distribution of Fourier coefficients to filter out relevant spectral points using an irrational window. Moreover, a corresponding index-shift transform is designed to make the Fast Fourier Transform available. The corresponding error analysis on the function appro…

“That's because kangaroos are completely irrational animals, said David Pickett, Volvo Australia’s technical lead.”
“Carmakers give up on software that avoids kangaroos”
#cars #animals #kangaroos

Carmakers give up on software that avoids kangaroos
Australia is turning to virtual fences to cut down on car-kangaroo impacts.

Continuum envelops on Fargues-Fontaine curves and elliptic curves
Heng Du, Qingyuan Jiang, Yucheng Liu
https://arxiv.org/abs/2404.04551 https://

Continuum envelops on Fargues-Fontaine curves and elliptic curves
In this paper, we apply the theory of Bridgeland stability conditions, which was originated from string theory, to study the derived category of coherent sheaves on Fargues--Fontaine curves. This leads us to consider the quasi-coherent sheaves $\mathcal{O}(θ^{\pm})$ via the convergents of an irrational number $θ$. We define the continuum envelop $\mathrm{QCoh}_{\mathbb{R}}(X_{FF})$ to be the smallest abelian subcategory in $\mathrm{QCoh}(X_{FF})$ containing $\mathrm{Coh}(X_{FF})$ and $\math…

On the representation of C-recursive integer sequences by arithmetic terms
Mihai Prunescu, Lorenzo Sauras-Altuzarra
https://arxiv.org/abs/2405.04083 https:…

On the representation of C-recursive integer sequences by arithmetic terms
We show that, if an integer sequence is given by a linear recurrence of constant rational coefficients, then it can be represented as the difference of two arithmetic terms with exponentiation, which do not contain any irrational constant. We apply our methods to various Lucas sequences including the classical Fibonacci sequence, to the sequence of solutions of the Pell equation and to some natural C-recursive sequences of degree 3.

A well-motivated proof that pi is irrational
Timothy Y. Chow
https://arxiv.org/abs/2403.20140 https://arxiv.org/pdf/2403.20140…

A well-motivated proof that pi is irrational
Ivan Niven's succinct proof that pi is irrational is easy to verify, but it begins with a magical formula that appears to come out of nowhere, and whose origin remains mysterious even after one goes through the proof. The goal of this expository paper is to describe a thought process by which a mathematician might come up with the proof from scratch, without having to be a genius. Compared to previous expositions of Niven's proof, perhaps the main novelty in the present account is an explicit a…

@… I hate to admit that you have excellent insight into the realities of my crazy project ideas. I know my fear of the death of the humanities is pretty irrational as @… pointed out, but I think something like this could be useful anyhow, just like how the Free Music Archive used to be useful to me.
I suspect a well-made database catalogue will be very important, as well as excellent search functionality and discoverability.
What gets me though, is, what even belongs in an archive??

Using finite automata to compute the base-$b$ representation of the golden ratio and other quadratic irrationals
Aaron Barnoff, Curtis Bright, Jeffrey Shallit
https://arxiv.org/abs/2405.02727

Using finite automata to compute the base-$b$ representation of the golden ratio and other quadratic irrationals
We show that the $n$'th digit of the base-$b$ representation of the golden ratio is a finite-state function of the Zeckendorf representation of $b^n$, and hence can be computed by a finite automaton. Similar results can be proven for any quadratic irrational. We use a satisfiability (SAT) solver to prove, in some cases, that the automata we construct are minimal.

Is there a specific math term for numbers in the open intervals (-1, 0) and/or (0,1)? 🤔 🤓
PS: There isn't anything deep about the interval, nature of numbers, etc. The numbers are just values of proper fractions. Exclude irrational numbers if you like but it doesn't matter unless it makes a difference for terminology, in that case please include that detail. 🙏🏽
I'm NOT a mathematician but have reasons to pose this question.

Mills' constant is irrational
Kota Saito
https://arxiv.org/abs/2404.19461 https://arxiv.org/pdf/2404.19461

Mills' constant is irrational
Let $\lfloor x\rfloor$ denote the integer part of $x$. In 1947, Mills constructed a real number $ξ$ greater than $1$ such that $\lfloor ξ^{3^k} \rfloor$ is always a prime number for every positive integer $k$. We define Mills' constant as the smallest real number $ξ$ satisfying this property. In this article, we determine that Mills' constant is irrational. Moreover, we also obtain partial results on the transcendency of the constant.

Irrational Random Utility Models
Daniele Caliari, Henrik Petri
https://arxiv.org/abs/2403.10208 https://arxiv.org/pdf/2403.10208

Irrational Random Utility Models
We show that the set of aggregate choices of a population of rational decision-makers - random utility models (RUMs) - can be represented by a population of irrational ones if, and only if, their preferences are sufficiently uncorrelated. We call this representation: Irrational RUM. We then show that almost all RUMs can be represented by a population in which at least some decision-makers are irrational and that under specific conditions their irrational behavior is unconstrained.

We’ve always been irrational and shortsighted beings. The only difference today is that our technological capabilities make that irrationality and shortsightedness existential threats for our species.

Accurate.

All people have lots of irrational feelings.
If we want to have a serious discussion about harm, prosecution, and imprisoning people we have a moral obligation to use reason and have a rational discussion.

On the representation of C-recursive integer sequences by arithmetic terms
Mihai Prunescu, Lorenzo Sauras-Altuzarra
https://arxiv.org/abs/2405.04083 https:…

On the representation of C-recursive integer sequences by arithmetic terms
We show that, if an integer sequence is given by a linear recurrence of constant rational coefficients, then it can be represented as the difference of two arithmetic terms with exponentiation, which do not contain any irrational constant. We apply our methods to various Lucas sequences including the classical Fibonacci sequence, to the sequence of solutions of the Pell equation and to some natural C-recursive sequences of degree 3.

This https://arxiv.org/abs/2403.16255 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Phase retrieval on circles and lines
Let $f$ and $g$ be analytic functions on the open unit disc $\mathbb D$ such that $|f|=|g|$ on a set $A$. We give an alternative proof of the result of Perez that there exists $c$ in the unit circle $\mathbb T$ such that $f=cg$ when $A$ is the union of two lines in $\mathbb D$ intersecting at an angle that is an irrational multiple of $π$, and from this deduce a sequential generalization of the result. Similarly, the same conclusion is valid when $f$ and $g$ are in the Neva…

Ach interessant, das 2021 verschwundene RPG Paranoia, Happiness is Mandatory gibt es seit Dezember wieder bei Steam. Gerade im Sale für 15 Euro. Erwarte davon nicht so viel, leider. Aber da ich es früher als PnP gespielt habe, schaue ich es mir man an. #Gaming #CRPG

Save 50% on Paranoia: Happiness is Mandatory on Steam
Lead a team of four Troubleshooters of dubious loyalty, who (mostly) obey orders from Friend Computer, a paranoid and irrational artificial intelligence. Inspired by the classic games of the CRPG genre, experience the first official adaptation of the cult role-playing game!

This https://arxiv.org/abs/2309.09012 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Modelling Irrational Behaviour of Residential End Users using Non-Stationary Gaussian Processes
Demand response (DR) plays a critical role in ensuring efficient electricity consumption and optimal use of network assets. Yet, existing DR models often overlook a crucial element, the irrational behaviour of electricity end users. In this work, we propose a price-responsive model that incorporates key aspects of end-user irrationality, specifically loss aversion, time inconsistency, and bounded rationality. To this end, we first develop a framework that uses Multiple Seasonal-Trend decomposit…

One can acclimate to wild stuff. For example: a persistent pervasive sense of inchoate impending doom. One learns not to pay attention to the baseline irrational paranoia and/or make fun of it. It does make MH screenings fun.

The socle of subshift algebras, with applications to subshift conjugacy
Daniel Gon\c{c}alves, Danilo Royer
https://arxiv.org/abs/2403.18806 https://…

The socle of subshift algebras, with applications to subshift conjugacy
We introduce the concept of "irrational paths" for a given subshift and use it to characterize all minimal left ideals in the associated unital subshift algebra. Consequently, we characterize the socle as the sum of the ideals generated by irrational paths. Proceeding, we construct a graph such that the Leavitt path algebra of this graph is graded isomorphic to the socle. This realization allows us to show that the graded structure of the socle serves as an invariant for the conjugacy of Ott-To…

This https://arxiv.org/abs/2404.01047 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the distribution of $αp+β$ modulo one for primes of type $p=ar^2+1$
A classical problem in analytic number theory is to study the distribution of fractional part $αp+β$ modulo 1, where $α$ is irrational and $p$ runs over the set of primes. We consider the subsequence generated by the primes $p$ such that $p=ar^2+1$ and prove that its distribution has a similar property.

This https://arxiv.org/abs/2301.01496 has been replaced.
link: https://scholar.google.com/scholar?q=a

Unique ergodicity of simple symmetric random walks on the circle
Fix an irrational number $α$ and a smooth, positive, real function $\mathfrak{p}$ on the circle. If current position is $x\in \mathbb R/\mathbb Z$ then in the next step jump to $x+α$ with probability $\mathfrak{p}(x)$ or to $x-α$ with probability $1-\mathfrak{p}(x)$. In 1999 Sinai has proven that if $\mathfrak{p}$ is asymmetric (in certain sense) or $α$ is Diophantine then the Markov process possesses a unique stationary distribution. Next year Conze and Guivarc'h showed the uniqueness of s…

This https://arxiv.org/abs/2404.01047 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the distribution of $αp+β$ modulo one for primes of type $p=ar^2+1$
A classical problem in analytic number theory is to study the distribution of fractional part $αp+β$ modulo 1, where $α$ is irrational and $p$ runs over the set of primes. We consider the subsequence generated by the primes $p$ such that $p=ar^2+1$ and prove that its distribution has a similar property.

If someone is being irrational (which is extremely common when discussing emotionally charged issues) sometimes it really helps to just point out the fact that they are reacting emotionally and have zero rational basis for their conclusions.

The Mixed Integer Trust Region Problem
Alberto Del Pia
https://arxiv.org/abs/2402.08827 https://arxiv.org/pdf/2402.08827

The Mixed Integer Trust Region Problem
In this paper we consider the problem of minimizing a general quadratic function over the mixed integer points in an ellipsoid. This problem is strongly NP-hard, NP-hard to approximate within a constant factor, and optimal solutions can be irrational. In our main result we show that an arbitrarily good solution can be found in polynomial time, if we fix the number of integer variables. This algorithm provides a natural extension to the mixed integer setting, of the polynomial solvability of the…

This https://arxiv.org/abs/2305.06257 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Elliptic Reeb orbit on some real projective three-spaces via ECH
We prove the existence of an elliptic Reeb orbit for some contact forms on the real projective three space $\mathbb{R} P^3$. The main ingredient of the proof is the existence of a distinguished pseudoholomorphic curve in the symplectization given by the $U$ map on ECH. Also, we check that the first value on the ECH spectrum coincides with the smallest action of null-homologous orbit sets for $1/4$-pinched Riemannian metrics and compute the ECH spectrum for the irrational Katok metric example.

An evolutionary game with reputation-based imitation-mutation dynamics
Kehuan Feng, Songlin Han, Minyu Feng, Attila Szolnoki
https://arxiv.org/abs/2402.13011

An evolutionary game with reputation-based imitation-mutation dynamics
Reputation plays a crucial role in social interactions by affecting the fitness of individuals during an evolutionary process. Previous works have extensively studied the result of imitation dynamics without focusing on potential irrational choices in strategy updates. We now fill this gap and explore the consequence of such kind of randomness, or one may interpret it as an autonomous thinking. In particular, we study how this extended dynamics alters the evolution of cooperation when individua…

This https://arxiv.org/abs/2311.00665 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Surface Geometry of Some Meaningful Extreme Kerr-Newman Black Holes
We address the properties of extremal black holes by considering the Christodoulou-Ruffini/Hawking mass-energy formula. By simple geometrical arguments, we found that the mass/energy formula is satisfied by two meaningful extremal black holes where mass (m), charge (Q), and angular momentum/spin (L) are proportional to the black holes irreducible mass (m_{ir}) expressed by irrational numbers. These black holes have been studied in the Christodoulou diagram and their topology in E^3 has been inv…

This https://arxiv.org/abs/2404.04507 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Irrational-window-filter projection method and application to quasiperiodic Schrödinger eigenproblems
In this paper, we propose a new algorithm, the irrational-window-filter projection method (IWFPM), for solving arbitrary dimensional global quasiperiodic systems. Based on the projection method, IWFPM further utilizes the concentrated distribution of Fourier coefficients to filter out relevant spectral points using an irrational window. Moreover, a corresponding index-shift transform is designed to make the Fast Fourier Transform available. The corresponding error analysis on the function appro…

This https://arxiv.org/abs/2404.01045 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the distribution of $αp^2+β$ modulo one for primes $p$ such that $p+2$ has no more two prime divisors
A classical problem in analytic number theory is to study the distribution of fractional part $αp^k+β,\,k\ge 1$ modulo 1, where $α$ is irrational and $p$ runs over the set of primes. For $k=2$ we consider the subsequence generated by the primes $p$ such that $p+2$ is an almost-prime (the existence of infinitely many such $p$ is another topical result in prime number theory) and prove that its distribution has a similar property.

This https://arxiv.org/abs/2104.01529 has been replaced.
link: https://scholar.google.com/scholar?q=a

Dirichlet forms on unconstrained Sierpinski carpets
We construct symmetric self-similar Dirichlet forms on unconstrained Sierpinski carpets, which are natural extension of planar Sierpinski carpets by allowing the small cells to live off the $1/k$ grids. The intersection of two cells can be a line segment of irrational length, and the non-diagonal assumption is dropped in this recurrent setting.

This https://arxiv.org/abs/2404.01045 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the distribution of $αp^2+β$ modulo one for primes $p$ such that $p+2$ has no more two prime divisors
A classical problem in analytic number theory is to study the distribution of fractional part $αp^k+β,\,k\ge 1$ modulo 1, where $α$ is irrational and $p$ runs over the set of primes. For $k=2$ we consider the subsequence generated by the primes $p$ such that $p+2$ is an almost-prime (the existence of infinitely many such $p$ is another topical result in prime number theory) and prove that its distribution has a similar property.

This https://arxiv.org/abs/2304.12286 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On local delta invariant of del Pezzo surfaces
We complete the classification of local stability thresholds for smooth del Pezzo surfaces of degree~2. In particular, we show that this number is irrational if and only if a unique (-1)-curve passes through the point where we are computing the local invariant.

This https://arxiv.org/abs/2403.16255 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Phase retrieval on circles and lines
Let $f$ and $g$ be analytic functions on the open unit disc $\mathbb D$ such that $|f|=|g|$ on various sets $A$. We first prove that there exists $c$ in the unit circle $\mathbb T$ such that $f=cg$ when $A$ is the union of two lines in $\mathbb D$ intersecting at an angle that is an irrational multiple of $π$. The same conclusion is valid when $f$ and $g$ are in the Nevanlinna class and $A$ is the union of the unit circle and an interior circle, tangential or not. We also p…

Forcing techniques for Cicho\'n's Maximum: Lecture notes for the mini-course at the University of Vienna
Diego A. Mej\'ia
https://arxiv.org/abs/2402.11852

Forcing techniques for Cichoń's Maximum: Lecture notes for the mini-course at the University of Vienna
Cichoń's diagram describes the connections between combinatorial notions related to measure, category, and compactness of sets of irrational numbers. In the second part of the 2010's decade, Goldstern, Kellner and Shelah constructed a forcing model of Cichoń's Maximum (meaning that all non-dependent cardinal characteristics are pairwise different) by using large cardinals. Some years later, we eliminated this large cardinal assumption. In this mini-course, we explore the forcing techniques to…

This https://arxiv.org/abs/2309.14646 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Concentration of dimension in extremal points of left-half lines in the Lagrange spectrum
We prove that for any $η$ that belongs to the closure of the interior of the Markov and Lagrange spectra, the sets $k^{-1}((-\infty,η])$ and $k^{-1}(η)$, which are the sets of irrational numbers with best constant of Diophantine approximation bounded by $η$ and exactly $η$ respectively, have the same Hausdorff dimension. We also show that, as $η$ varies in the interior of the spectra, this Hausdorff dimension is a strictly increasing function.

This https://arxiv.org/abs/2403.16255 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Phase retrieval on circles and lines
Let $f$ and $g$ be analytic functions on the open unit disc $\mathbb D$ such that $|f|=|g|$ on various sets $A$. We first prove that there exists $c$ in the unit circle $\mathbb T$ such that $f=cg$ when $A$ is the union of two lines in $\mathbb D$ intersecting at an angle that is an irrational multiple of $π$. The same conclusion is valid when $f$ and $g$ are in the Nevanlinna class and $A$ is the union of the unit circle and an interior circle, tangential or not. We also p…

This https://arxiv.org/abs/2306.12602 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qfi…

Social Media Emotions and IPO Returns
I examine potential mechanisms behind two stylized facts of initial public offerings (IPOs) returns. By analyzing investor emotions expressed on StockTwits and Twitter, I find that emotions conveyed through these social media platforms can help explain the mispricing of IPO stocks. The abundance of information and opinions shared on social media can generate hype around certain stocks, leading to investors' irrational buying and selling decisions. This can result in an overvaluation of the stoc…

This https://arxiv.org/abs/2309.14646 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Concentration of dimension in extremal points of left-half lines in the Lagrange spectrum
We prove that for any $η$ that belongs to the closure of the interior of the Markov and Lagrange spectra, the sets $k^{-1}((-\infty,η])$ and $k^{-1}(η)$, which are the sets of irrational numbers with best constant of Diophantine approximation bounded by $η$ and exactly $η$ respectively, have the same Hausdorff dimension. We also show that, as $η$ varies in the interior of the spectra, this Hausdorff dimension is a strictly increasing function.

Phase retrieval on circles and lines
I. Chalendar, J. R. Partington
https://arxiv.org/abs/2403.16255 https://arxiv.org/pdf/2403.16255…

Phase retrieval on circles and lines
Let $f$ and $g$ be analytic functions on the open unit disc $\mathbb D$ such that $|f|=|g|$ on various sets $A$. We first prove that there exists $c$ in the unit circle $\mathbb T$ such that $f=cg$ when $A$ is the union of two lines in $\mathbb D$ intersecting at an angle that is an irrational multiple of $π$. The same conclusion is valid when $f$ and $g$ are in the Nevanlinna class and $A$ is the union of the unit circle and an interior circle, tangential or not. We also p…

This https://arxiv.org/abs/1608.04106 has been replaced.
link: https://scholar.google.com/scholar?q=a

The high type quadratic Siegel disks are Jordan domains
Let $α$ be an irrational number of sufficiently high type and suppose $P_α(z)=e^{2πiα}z+z^2$ has a Siegel disk $Δ_α$ centered at the origin. We prove that the boundary of $Δ_α$ is a Jordan curve, and that it contains the critical point $-e^{2πiα}/2$ if and only if $α$ is a Herman number.

Diophantine approximation by rational numbers of certain parity types
Dong Han Kim, Seul Bee Lee, Lingmin Liao
https://arxiv.org/abs/2403.12341 https://

Diophantine approximation by rational numbers of certain parity types
For a given irrational number, we consider the properties of best rational approximations of given parities. There are three different kinds of rational numbers according to the parity of the numerator and denominator, say odd/odd, even/odd and odd/even rational numbers. We study algorithms to find best approximations by rational numbers of given parities and compare these algorithms with continued fraction expansions.

This https://arxiv.org/abs/2302.13308 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Poissonian pair correlation for directions in multi-dimensional affine lattices, and escape of mass estimates for embedded horospheres
We prove the convergence of moments of the number of directions of affine lattice vectors that fall into a small disc, under natural Diophantine conditions on the shift. Furthermore, we show that the pair correlation function is Poissonian for any irrational shift in dimension 3 and higher, including well-approximable vectors. Convergence in distribution was already proved in the work of Strömbergsson and the second author, and the principal step in the extension to convergence of moments is a…

This https://arxiv.org/abs/2111.06139 has been replaced.
link: https://scholar.google.com/scholar?q=a

Asymptotic distribution for pairs of linear and quadratic forms at integral vectors
We study the joint distribution of values of a pair consisting of a quadratic form $q$ and a linear form $\mathbf l$ over the set of integral vectors, a problem initiated by Dani-Margulis (1989). In the spirit of the celebrated theorem of Eskin, Margulis and Mozes on the quantitative version of the Oppenheim conjecture, we show that if $n \ge 5$ then under the assumptions that for every $(α, β) \in \mathbb R^2 \setminus \{ (0,0) \}$, the form $αq + β\mathbf l^2$ is irrational and that the s…