Results 21 to 30 of about 58 (55)
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
Short addition sequences for theta functions [PDF]
, 2018 International audienceThe main step in numerical evaluation of classical Sl2 (Z) modular forms and elliptic functions is to compute the sum of the first N nonzero terms in the sparse q-series belonging to the Dedekind eta function or the Jacobi theta ...
Hart, William +2 more
core +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
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 +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 +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