Results 11 to 20 of about 1,505 (62)
A dichotomy for extreme values of zeta and Dirichlet L$L$‐functions
Bulletin of the London Mathematical Society, Volume 55, Issue 6, Page 2963-2975, December 2023., 2023 Abstract We exhibit large values of the Dedekind zeta function of a cyclotomic field on the critical line. This implies a dichotomy whereby one either has improved lower bounds for the maximum of the Riemann zeta function, or large values of Dirichlet L$L$‐functions on the level of the Bondarenko–Seip bound.
Andriy Bondarenko +4 more
wiley +1 more source
A P‐adic class formula for Anderson t‐modules
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract In 2012, Taelman proved a class formula for L$L$‐series associated to Drinfeld Fq[θ]$\mathbb {F}_q[\theta]$‐modules and considered it as a function field analogue of the Birch and Swinnerton‐Dyer conjecture. Since then, Taelman's class formula has been generalized to the setting of Anderson t$t$‐modules.
Alexis Lucas
wiley +1 more source
Fusion systems related to polynomial representations of SL2(q)$\operatorname{SL}_2(q)$
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract Let q$q$ be a power of a fixed prime p$p$. We classify up to isomorphism all simple saturated fusion systems on a certain class of p$p$‐groups constructed from the polynomial representations of SL2(q)$\operatorname{SL}_2(q)$, which includes the Sylow p$p$‐subgroups of GL3(q)$\mathrm{GL}_3(q)$ and Sp4(q)$\mathrm{Sp}_4(q)$ as special cases.
Valentina Grazian +3 more
wiley +1 more source
Fractional moments of L$L$‐functions and sums of two squares in short intervals
Mathematika, Volume 71, Issue 4, October 2025.Abstract Let b(n)=1$b(n)=1$ if n$n$ is the sum of two perfect squares, and b(n)=0$b(n)=0$ otherwise. We study the variance of B(x)=∑n⩽xb(n)$B(x)=\sum _{n\leqslant x}b(n)$ in short intervals by relating the variance with the second moment of the generating function f(s)=∑n=1∞b(n)n−s$f(s)=\sum _{n=1}^{\infty } b(n)n^{-s}$ along Re(s)=1/2$\mathrm{Re}(s)=1/
Siegfred Baluyot, Steven M. Gonek
wiley +1 more source
Counting primes with a given primitive root, uniformly
Mathematika, Volume 71, Issue 4, October 2025.Abstract The celebrated Artin conjecture on primitive roots asserts that given any integer g$g$ that is neither −1$-1$ nor a perfect square, there is an explicit constant A(g)>0$A(g)>0$ such that the number Π(x;g)$\Pi (x;g)$ of primes p⩽x$p\leqslant x$ for which g$g$ is a primitive root is asymptotically A(g)π(x)$A(g)\pi (x)$ as x→∞$x\rightarrow \infty$
Kai (Steve) Fan, Paul Pollack
wiley +1 more source
Parity of ranks of Jacobians of curves
Proceedings of the London Mathematical Society, Volume 131, Issue 3, September 2025.Abstract We investigate Selmer groups of Jacobians of curves that admit an action of a non‐trivial group of automorphisms, and give applications to the study of the parity of Selmer ranks. Under the Shafarevich–Tate conjecture, we give an expression for the parity of the Mordell–Weil rank of an arbitrary Jacobian in terms of purely local invariants ...
Vladimir Dokchitser +3 more
wiley +1 more source
On Artin's conjecture on average and short character sums
Bulletin of the London Mathematical Society, Volume 57, Issue 8, Page 2429-2443, August 2025.Abstract Let Na(x)$N_a(x)$ denote the number of primes up to x$x$ for which the integer a$a$ is a primitive root. We show that Na(x)$N_a(x)$ satisfies the asymptotic predicted by Artin's conjecture for almost all 1⩽a⩽exp((loglogx)2)$1\leqslant a\leqslant \exp ((\log \log x)^2)$. This improves on a result of Stephens (1969).
Oleksiy Klurman +2 more
wiley +1 more source
Arithmetic Satake compactifications and algebraic Drinfeld modular forms
Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.Abstract In this article, we construct the arithmetic Satake compactification of the Drinfeld moduli schemes of arbitrary rank over the ring of integers of any global function field away from the level structure, and show that the universal family extends uniquely to a generalized Drinfeld module over the compactification.
Urs Hartl, Chia‐Fu Yu
wiley +1 more source
An Elliptic Analogue Of Generalized Cotangent Dirichlet Series And Its Transformation Formulae At Some Integer Arguments [PDF]
, 2011 B.C. Berndt evaluated special values of the cotangent Dirichlet series. T. Arakawa studied a generalization of the series, or generalized cotangent Dirichlet series, and gave its transformation formulae.
Machide, T.
core
Identities for generalized Appell functions and the blow-up formula
, 2015 In this paper, we prove identities for a class of generalized Appell functions which are based on the $\operatorname{A}_2$ root lattice. The identities are reminiscent of periodicity relations for the classical Appell function, and are proven using only ...
Bringmann, Kathrin +2 more
core +1 more source