Tootfinder

Construction of Higher Chow cycles on cyclic coverings of $\mathbb{P}^1 \times \mathbb{P}^1$
Yusuke Nemoto, Ken Sato
https://arxiv.org/abs/2509.05569 https://

Construction of Higher Chow cycles on cyclic coverings of $\mathbb{P}^1 \times \mathbb{P}^1$
In this paper, we construct higher Chow cycles of type $(2, 1)$ on a certain family of surfaces, which are constructed by a product of certain hypergeometric curves of degree $N$. We prove that for a very general member, these cycles are linearly independent over $\mathbb{Z}$ and generate a subgroup of $\operatorname{rank} \ge 36 \cdot φ(N)$, where $φ(N)$ is Euler's totient function, by computing the image of the transcendental regulator map.

Urban Solitude IV 🈳
城市孤独 IV 🈳
📷 Pentax MX
🎞️Fujifilm Neopan SS, expired 1995
buy me ☕️ ?/请我喝杯☕️？
#filmphotography

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What a nice loop this was!
Lot's of cyclists on the main roads. Seems like everyone is enjoying the weather 😊
#cycling #mountainbiking #mtb

The determination of norm-Euclidean cyclic cubic fields
Gustav Kj{\ae}rbye Bagger, Andrew R. Booker, Bryce Kerr, Kevin McGown, Valeriia Starichkova, Tim Trudgian
https://arxiv.org/abs/2507.05862

The determination of norm-Euclidean cyclic cubic fields
It is known on the Generalised Riemann Hypothesis that there are precisely $13$ cyclic cubic fields that are norm-Euclidean. Unconditionally, there is a gap between analytic estimates which hold for all sufficiently large conductors and computational techniques. In this paper, we establish new results concerning explicit bounds for cubic non-residues and refine previous computational techniques, enabling us to completely characterise all norm-Euclidean cyclic cubic fields.

The discontinuous planar piecewise linear system with two nodes has at most two limit cycles
Lu Chen, Changjian Liu
https://arxiv.org/abs/2506.07716 https:…

The discontinuous planar piecewise linear system with two nodes has at most two limit cycles
This paper investigates the multiplicity and the number of limit cycles for planar piecewise linear system divided into two regions by a straight line and each linear subsystem has a node. Through constructing Poincare half maps and a successor function, and analyzing the properties of the successor function, we can derive that this system has at most two limit cycles, counting the multiplicities of limit cycles.

A Class of Cyclic Quantum Codes
Matthew B. Hastings
https://arxiv.org/abs/2509.06865 https://arxiv.org/pdf/2509.06865…

A Class of Cyclic Quantum Codes
We introduce a class of cyclic quantum codes, basing the construction not on the simplicity of the stabilizers, but rather on the simplicity of preparation of a code state (at least in the absence of noise). We show how certain known codes, such as a certain family of rotated two-dimensional toric codes, fall into this class, and we also give certain other examples at small sizes found by computer search. We finally discuss fault tolerant preparation of these codes.

alright im going through my old files again and rediscovered a shitty unfinished sci-fi epic poem thing i was writing sometime when i was 14/15/idfk. all i remember about it is that it was gonna keep doing this countdown and changing structure accordingly for a really long time, i was thinking of depicting the character finding love in an ethereal sorta way for the ending, and it was gonna incorporate a enochian number square for some reason.

Cyclic codes of length $n$ over finite chain rings
Seema Antil, Gurleen Kaur, Manju Khan
https://arxiv.org/abs/2509.06397 https://arxiv.org/pdf/2509.06397

Cyclic codes of length $n$ over finite chain rings
In this paper, the cyclic codes of length $n$, where $n$ is odd with certain restrictions, over a finite chain ring $R$, have been studied using the structure of group algebra approach. The primitive idempotents of $RG$ of a finite cyclic group $G$ have been determined, and then the number of codewords and the minimum weight corresponding to a cyclic code have been computed.

Existence of simple non-cyclic abelian varieties over arbitrary finite fields and of a given dimension $g>1$
Alejandro J. Giangreco Maidana
https://arxiv.org/abs/2507.06916

Existence of simple non-cyclic abelian varieties over arbitrary finite fields and of a given dimension $g>1$
Vl{\u a}du{\c t} characterized in 1999 the set of finite fields $k$ such that all elliptic curves defined over $k$ have a cyclic group of rational points. Under the conjecture of infinitely many Mersenne primes, this set is infinite. In these notes we prove that there is no a finite field $k$ such that all the simple abelian varieties defined over $k$ of dimension $g>1$ have a cyclic group of rational points.

Urban Solitude V 🈳
城市孤独 V 🈳
📷 Pentax MX
🎞️Fujifilm Neopan SS, expired 1995
buy me ☕️ ?/请我喝杯☕️？
#filmphotography

Yiding Cao Geld mit PayPal.Me senden
Folgen Sie dem Link PayPal.Me/dingsterdingster und geben Sie den Betrag ein. Es ist bequem und sicher. Sie haben noch kein PayPal-Konto? Kein Problem.