Exponential sums with Dirichlet coefficients of L-functions

2012/06/22 by Stephan Baier, Baier, Stephan
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1206.5039

openalex publication_date 2012/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Improving and extending recent results of the author, we conditionally estimate exponential sums with Dirichlet coefficients of L-functions, both over all integers and over all primes in an interval. In particular, we establish new conditional results on exponential sums with Hecke eigenvalues and squares of Hecke eigenvalues over primes. We employ these estimates to improve our recent result on squares of Hecke eigenvalues at Piatetski-Shapiro primes under the Riemann Hypothesis for symmetric square L-functions for Hecke eigenforms.

Related

• Exponential sums with coefficients of certain Dirichlet series
• A conditional result on exponential sums over primes in short intervals
• L-functions of Certain Exponential Sums over Finite Fields
• A Bombieri-Vinogradov theorem for exponential sums over products of k primes
• An arithmetic formula for certain coefficients of the Euler product of Hecke polynomials