Tootfinder

On Triple Quadratic Residue Symbols in Real Quadratic Fields
Atsuki Kuramoto
https://arxiv.org/abs/2509.00667 https://arxiv.org/pdf/2509.00667

On Triple Quadratic Residue Symbols in Real Quadratic Fields
We introduce triple quadratic residue symbols $[\mathfrak{p}_1, \mathfrak{p}_2, \mathfrak{p}_3]$ for certain finite primes $\mathfrak{p}_i$'s of a real quadratic field $k$ with trivial narrow class group. For this, we determine a presentation of the Galois group of the maximal pro-2 Galois extension over $k$ unramified outside $\mathfrak{p}_1, \mathfrak{p}_2, \mathfrak{p}_3$ and infinite primes, from which we derive mod 2 arithmetic triple Milnor invariants $μ_2(123)$ yielding the triple symbo…

Attack Detection in Dynamic Games with Quadratic Measurements
Muyan Jiang, Anil Aswani
https://arxiv.org/abs/2510.00241 https://arxiv.org/pdf/2510.00241

Attack Detection in Dynamic Games with Quadratic Measurements
This paper studies attack detection for discrete-time linear systems with stochastic process noise that produce both a vulnerable (i.e., attackable) linear measurement and a secured (i.e., unattackable) quadratic measurement. The motivating application of this model is a dynamic-game setting where the quadratic measurement is interpreted as a system-level utility or reward, and control inputs into the linear system are interpreted as control policies that, once applied, are known to all game pa…

Unser zweierlei Maß bei #Enteignung:
Super böse, wenn damit sichere Radwege gebaut werden. Privateigentum ist dann ein hohes Gut.
Super toll, wenn man damit auf der grünen Wiese Neubaugebiete erschließen will.
Im Ort Rastorf beschließt der Rat aus zwei lokalen Listen und CDU einstimmig bei einer Enthaltung ein Enteignungsverfahren, um ein Neubaugebiet zu erschließen, obwohl di…

Enteignung in Rastorf? „Selbst wenn ich 80.000 Euro bekäme, ich wäre nicht käuflich“
Silke Wilde soll ihr Grundstück verkaufen. Die Rastorferin besitzt 267 Quadratmeter auf dem Düsternbrook, über den die Gemeinde ein Baugebiet erschließen möchte. Doch Silke Wilde wehrt sich wie eine Löwin – auch gegen eine mögliche Enteignung.

The Constant Speed Schedule for Adiabatic State Preparation: Towards Quadratic Speedup without Prior Spectral Knowledge
Mancheon Han, Hyowon Park, Sangkook Choi
https://arxiv.org/abs/2510.01923

The Constant Speed Schedule for Adiabatic State Preparation: Towards Quadratic Speedup without Prior Spectral Knowledge
The efficiency of adiabatic quantum evolution is governed by the adiabatic evolution time, \(T\), which depends on the minimum energy gap, \(Δ\). For a generic schedule, \(T\) typically scales as \(Δ^{-2}\), whereas the rigorous lower bound is \(\mathcal{O}(Δ^{-1})\). This indicates the potential for a quadratic speedup through the adiabatic schedule construction. Here, we introduce the constant speed schedule, which traverses the adiabatic path of the eigenstate at a uniform rate. We first …

Quadratic equations of tangent varieties via four-way tensors of linear forms
Junho Choe
https://arxiv.org/abs/2510.01908 https://arxiv.org/pdf/2510.01908

Quadratic equations of tangent varieties via four-way tensors of linear forms
In the present paper we construct quadratic equations and linear syzygies for tangent varieties using 4-way tensors of linear forms and generalize this method to higher secant varieties of higher osculating varieties. Such equations extend the classical determinantal ones of higher secant varieties and span all the equations of the same degree for smooth projective curves completely embedded by sufficiently positive line bundles, proving a variant of the Eisenbud-Koh-Stillman conjecture on dete…

Composite Generalized Quadratic Noise Modulation via Signal Addition: Towards Higher Dimensional Noise Modulations
Hadi Zayyani, Mohammad Salman, Felipe A. P. de Figueiredo, Rausley A. A. de Souza
https://arxiv.org/abs/2510.01776

Composite Generalized Quadratic Noise Modulation via Signal Addition: Towards Higher Dimensional Noise Modulations
This letter proposes superposing two Generalized Quadratic Noise Modulators (GQNM) by simply adding their outputs. It creates a 16-ary noise modulator that resembles QAM modulators in classical communication. It modulates the information bits on four different means and four different variances. It could also be applied to reach higher-order modulations than 16-ary schemes by adding the outputs of more than two modulators, which is not discussed in detail in this letter and left for future work…

London is establishing itself as a center for quantitative finance; filings show trading firms XTX, Qube, and Quadrature each made £1B revenue in the past year (Financial Times)
https://www.ft.com/content/8a6502c3-f244-4b61-880b-b20cf03299cc

Quadratic Chabauty for Atkin-Lehner quotients of modular curves via weakly holomorphic modular forms: Hodge Filtrations
Isabel Rendell
https://arxiv.org/abs/2509.02291 https://

Quadratic Chabauty for Atkin-Lehner quotients of modular curves via weakly holomorphic modular forms: Hodge Filtrations
For Atkin-Lehner quotients $X_0^+(N)$, of prime level and of genus at least 2, we provide an algorithm for computing one of the main objects in the quadratic Chabauty algorithm in terms of weakly holomorphic modular forms associated to the curve. In particular, the algorithm computes a Hodge filtration on a certain unipotent vector bundle with connection related to $X_0^+(N)$, which is crucial in computing the $p$-adic height which is used to define the finite set of $p$-adic points containing …

A parametrization of $3$-class groups of quadratic rings over Dedekind domains
Eliot Hodges, Ashvin A. Swaminathan
https://arxiv.org/abs/2509.01722 https://

A parametrization of $3$-class groups of quadratic rings over Dedekind domains
Let $R$ be a Dedekind domain with field of fractions $K$ and $\operatorname{char}(R)\neq3$. In this paper, we generalize Bhargava's parametrization of $3$-torsion ideal classes by binary cubic forms to work over $R$. Specifically, we construct arithmetic subgroups of $\operatorname{GL}_2(K)$ whose actions on certain lattices of binary cubic forms over $K$ parametrize $3$-torsion ideal classes in class groups of quadratic rings over $R$.

On the Birch and Swinnerton-Dyer formula modulo squares for certain quadratic twists of elliptic curves
Alexander J. Barrios, Chung Pang Mok
https://arxiv.org/abs/2510.00926 htt…

On the Birch and Swinnerton-Dyer formula modulo squares for certain quadratic twists of elliptic curves
Let $E/\mathbb{Q}$ be an elliptic curve with conductor $N=N_+N_-$, where $N_+$ and $N_-$ are coprime and $N_-$ is squarefree. Let $D$ be a positive fundamental discriminant satisfying the modified Heegner hypothesis with respect to $(N_+,N_-)$: primes dividing $N_+$ (resp. $N_-$) split (resp. are inert) in $\mathbb{Q}(\sqrt{D})$; we denote by $E^D/\mathbb{Q}$ the quadratic twist of $E/\mathbb{Q}$ by $D$. In the first half of the paper we consider the situation where $N_-$ is a squarefree produc…