Results 21 to 30 of about 28,720,463 (113)

Zeros of quadratic Dirichlet $L$-functions in the hyperelliptic ensemble [PDF]

Transactions of the American Mathematical Society, 2016
We study the $1$-level density and the pair correlation of zeros of quadratic Dirichlet $L$-functions in function fields, as we average over the ensemble $\mathcal{H}_{2g+1}$ of monic, square-free polynomials with coefficients in $\mathbb{F}_q[x]$.
H. Bui, Alexandra Florea
semanticscholar   +1 more source

Shtukas and the Taylor expansion of L-functions (II) [PDF]

Annals of Mathematics, 2015
For arithmetic applications, we extend and refine our results in \cite{YZ} to allow ramifications in a minimal way. Starting with a possibly ramified quadratic extension $F'/F$ of function fields over a finite field in odd characteristic, and a finite ...
Zhiwei Yun, Wei Zhang
semanticscholar   +1 more source

The mean value of symmetric square $L$-functions [PDF]

, 2016
This paper studies the first moment of symmetric-square $L$-functions at the critical point in the weight aspect. Asymptotics with the best known error term $O(k^{-1/2})$ were obtained independently by Fomenko in 2005 and by Sun in 2013.
O. Balkanova, D. Frolenkov
semanticscholar   +1 more source

Joint universality for dependent L-functions

The Ramanujan journal, 2017
We prove that, for arbitrary Dirichlet L-functions L(s;χ1),…,L(s;χn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek ...
Łukasz Pańkowski
semanticscholar   +1 more source

Weyl-type hybrid subconvexity bounds for twisted $L$-functions and Heegner points on shrinking sets [PDF]

, 2014
We prove a Weyl-type subconvexity bound for the central value of the $L$-function of a Hecke-Maass form or a holomorphic Hecke eigenform twisted by a quadratic Dirichlet character, uniform in the archimedean parameter as well as the twisting parameter. A
M. Young
semanticscholar   +1 more source

On moments of twisted L-functions [PDF]

, 2014
We study the average of the product of the central values of two $L$-functions of modular forms $f$ and $g$ twisted by Dirichlet characters to a large prime modulus $q$.
V. Blomer, É. Fouvry, E. Kowalski, P. Michel, Djordje Milićević   +4 more
semanticscholar   +1 more source

Conjectures for the integral moments and ratios of L-functions over function fields [PDF]

, 2014
We extend to the function field setting the heuristic previously developed, by Conrey, Farmer, Keating, Rubinstein and Snaith, for the integral moments and ratios of L-functions defined over number fields.
J. Andrade, J. Keating
semanticscholar   +1 more source

A survey on the theory of universality for zeta and $L$-functions [PDF]

, 2014
We survey the results and the methods in the theory of universality for various zeta and $L$-functions, obtained in these forty years after the first discovery of the universality for the Riemann zeta-function by Voronin.
Kohji Matsumoto
semanticscholar   +1 more source

P ‐adic L ‐functions of Bianchi modular forms [PDF]

, 2014
The theory of overconvergent modular symbols, developed by Rob Pollack and Glenn Stevens, gives a beautiful and effective construction of the p ‐adic L ‐function of a modular form.
Chris Williams
semanticscholar   +1 more source

Critical values of Rankin-Selberg L-functions for GL(n) x GL(n-1) and the symmetric cube L-functions for GL(2) [PDF]

, 2013
In a previous article we had proved an algebraicity result for the central critical value for L-functions for GL(n) x GL(n-1) over Q assuming the validity of a nonvanishing hypothesis involving archimedean integrals.
A. Raghuram
semanticscholar   +1 more source