Results 41 to 50 of about 229 (136)

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, Igor E. Shparlinski, Joni Teräväinen   +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

Twisted conjugacy in soluble arithmetic groups

Mathematische Nachrichten, Volume 298, Issue 3, Page 763-793, March 2025.
Abstract Reidemeister numbers of group automorphisms encode the number of twisted conjugacy classes of groups and might yield information about self‐maps of spaces related to the given objects. Here, we address a question posed by Gonçalves and Wong in the mid‐2000s: we construct an infinite series of compact connected solvmanifolds (that are not ...
Paula M. Lins de Araujo, Yuri Santos Rego   +1 more
wiley   +1 more source

Laurent expansions of meromorphic modular forms

Journal of the London Mathematical Society, Volume 110, Issue 6, December 2024.
Abstract In this paper, we study the Laurent coefficients of meromorphic modular forms at complex multiplication points by giving two approaches of computing them. The first is a generalization of the method of Rodriguez‐Villegas and Zagier, which expresses the Laurent coefficients as constant terms of a family of polynomials obtained through recursion.
Gabriele Bogo, Yingkun Li, Markus Schwagenscheidt   +2 more
wiley   +1 more source

The slice spectral sequence for a motivic analogue of the connective K(1)$K(1)$‐local sphere

Proceedings of the London Mathematical Society, Volume 129, Issue 5, November 2024.
Abstract We compute the 2‐adic effective slice spectral sequence (ESSS) for the motivic stable homotopy groups of L$L$, a motivic analogue of the connective K(1)$K(1)$‐local sphere over prime fields of characteristic not two. Together with the analogous computation over algebraically closed fields, this yields information about the motivic K(1)$K(1 ...
Hana Jia Kong, J. D. Quigley
wiley   +1 more source

On tame ramification and centers of F$F$‐purity

Journal of the London Mathematical Society, Volume 110, Issue 4, October 2024.
Abstract We introduce a notion of tame ramification for general finite covers. When specialized to the separable case, it extends to higher dimensions the classical notion of tame ramification for Dedekind domains and curves and sits nicely in between other notions of tame ramification in arithmetic geometry. However, when applied to the Frobenius map,
Javier Carvajal‐Rojas, Anne Fayolle
wiley   +1 more source

POWERS OF THE DEDEKIND ETA FUNCTION AND HURWITZ POLYNOMIALS (Analytic and Arithmetic Theory of Automorphic Forms) [PDF]

, 2019
In this talk, we study the vanishing properties of Fourier coefficients of powers of the Dedekind eta function. We give a certain type of classification of this property. Further we extend the results of Atkin, Cohen, and Newman for odd powers and a list
Heim, Bernhard
core  

A discrete mean value of the Riemann zeta function

Mathematika, Volume 70, Issue 4, October 2024.
Abstract In this work, we estimate the sum ∑0<ℑ(ρ)⩽Tζ(ρ+α)X(ρ)Y(1−ρ)$$\begin{align*} \sum _{0 < \Im (\rho) \leqslant T} \zeta (\rho +\alpha)X(\rho) Y(1\!-\! \rho) \end{align*}$$over the nontrivial zeros ρ$\rho$ of the Riemann zeta function where α$\alpha$ is a complex number with α≪1/logT$\alpha \ll 1/\log T$ and X(·)$X(\cdot)$ and Y(·)$Y(\cdot)$ are ...
Kübra Benli, Ertan Elma, Nathan Ng
wiley   +1 more source

On the multipliersystem of the Riemann-Dedekind function \(\eta\) [PDF]

Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen: Series A: Mathematical Sciences, 1958
van Lint, J.H., Lint, JH van
openaire   +4 more sources

Semilinear clannish algebras

Proceedings of the London Mathematical Society, Volume 129, Issue 4, October 2024.
Abstract We define a class of associative algebras generalizing ‘clannish algebras’, as introduced by the second author, but also incorporating semilinear structure, like a skew polynomial ring. Clannish algebras generalize the well‐known ‘string algebras’ introduced by Butler and Ringel.
Raphael Bennett‐Tennenhaus, William Crawley‐Boevey   +1 more
wiley   +1 more source