Results 61 to 70 of about 13,182 (153)
Counting problems for orthogonal sets and sublattices in function fields
Mathematika, Volume 72, Issue 2, April 2026.Abstract Let K=Fq((x−1))$\mathcal {K}=\mathbb {F}_q((x^{-1}))$. Analogous to orthogonality in the Euclidean space Rn$\mathbb {R}^n$, there exists a well‐studied notion of ultrametric orthogonality in Kn$\mathcal {K}^n$. In this paper, we extend the work of [4] on counting problems related to orthogonality in Kn$\mathcal {K}^n$.
Noy Soffer Aranov, Angelot Behajaina
wiley +1 more source
The p-adic valuations of sequences counting alternating sign matrices
, 2009 The p-adic valuations of a sequence of integers T(n) counting alternating sign matrices is examined for p=2 and p=3. Symmetry properties of their graphs produce a new proof of the result that characterizes the indices for which T(n) is odd.
Sun, Xinyu, Moll, Victor H.
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Moments of L$L$‐functions via a relative trace formula
Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.Abstract We prove an asymptotic formula for the second moment of the GL(n)×GL(n−1)$\mathrm{GL}(n)\times \mathrm{GL}(n-1)$ Rankin–Selberg central L$L$‐values L(1/2,Π⊗π)$L(1/2,\Pi \otimes \pi)$, where π$\pi$ is a fixed cuspidal representation of GL(n−1)$\mathrm{GL}(n-1)$ that is tempered and unramified at every place, while Π$\Pi$ varies over a family of
Subhajit Jana, Ramon Nunes
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The $p$-Adic Valuation Trees for Quadratic Polynomials for Odd Primes
, 2023 We examine the behavior of the sequences of $p$-adic valuations of quadratic polynomials with integer coefficients for an odd prime $p$ through tree representations. Under this representation, a finite tree corresponds to a periodic sequence, and an infinite tree corresponds to an unbounded sequence.
Boultinghouse, Will +5 more
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Rational points in a family of conics over F2(t)$\mathbb {F}_2(t)$
Mathematische Nachrichten, Volume 299, Issue 3, Page 496-513, March 2026.Abstract Serre famously showed that almost all plane conics over Q$\mathbb {Q}$ have no rational point. We investigate versions of this over global function fields, focusing on a specific family of conics over F2(t)$\mathbb {F}_2(t)$ which illustrates new behavior.
Daniel Loughran, Judith Ortmann
wiley +1 more source
\(p\)-Adic Valuation of \(\prod_{k=m+1}^{n} (k^2-m^2)\)
, 2023 This paper presents the $p$-adic valuation of the sequence $C_n(m)=\prod_{k=m+1}^n(k^2-m^2),$ $n=m+1,m+2,\cdots.$ An explicit formula is derived for the $p$-adic valuation of $C_n(m).$ From an applicational perspective, this study proves that $C_n(m)$ is not a square when $m=2,3.$ Additionally, this paper provides a criterion for $C_n(m)$ being a ...
Jia, Chang-Kun, Niu, Chuan-Ze
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On quantum ergodicity for higher‐dimensional cat maps modulo prime powers
Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.Abstract A discrete model of quantum ergodicity of linear maps generated by symplectic matrices A∈Sp(2d,Z)$A \in \operatorname{Sp}(2d,{\mathbb {Z}})$ modulo an integer N⩾1$N\geqslant 1$, has been studied for d=1$d=1$ and almost all N$N$ by Kurlberg and Rudnick (2001, Comm. Math. Phys., 222, 201–227).
Subham Bhakta, Igor E. Shparlinski
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Zarankiewicz bounds from distal regularity lemma
Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.Abstract Since Kővári, Sós and Turán proved upper bounds for the Zarankiewicz problem in 1954, much work has been undertaken to improve these bounds, and some have done so by restricting to particular classes of graphs. In 2017, Fox, Pach, Sheffer, Suk and Zahl proved better bounds for semialgebraic binary relations, and this work was extended by Do in
Mervyn Tong
wiley +1 more source
p$p$‐adic equidistribution and an application to S$S$‐units
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract We prove a Galois equidistribution result for torsion points in Gmn$\mathbb {G}_m^n$ in the p$p$‐adic setting for test functions of the form log|F|p$\log |F|_p$ where F$F$ is a nonzero polynomial with coefficients in the field of complex p$p$‐adic numbers.
Gerold Schefer
wiley +1 more source
The L$L$‐polynomials of van der Geer–van der Vlugt curves in characteristic 2
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract The van der Geer–van der Vlugt curves form a class of Artin–Schreier coverings of the projective line over finite fields. We provide an explicit formula for their L$L$‐polynomials in characteristic 2, expressed in terms of characters of maximal abelian subgroups of the associated Heisenberg groups.
Tetsushi Ito +2 more
wiley +1 more source