Exponential sums with coefficients of certain Dirichlet series

Stephan Baier

doi:10.1007/s00605-011-0372-7

Exponential sums with coefficients of certain Dirichlet series

Stephan Baier

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Under the generalized Lindelöf Hypothesis in the t- and q-aspects, we bound exponential sums with coefficients of Dirichlet series belonging to a certain class. We use these estimates to establish a conditional result on squares of Hecke eigenvalues at Piatetski–Shapiro primes.

Original language	English
Pages (from-to)	127-143
Number of pages	17
Journal	Monatshefte für Mathematik
Volume	169
Issue number	2
Early online date	23 Dec 2011
DOIs	https://doi.org/10.1007/s00605-011-0372-7
Publication status	Published - Feb 2013

Keywords

Exponential sums
Dirichlet series
Hecke eigenvalues
Piatetski–Shapiro primes

Access to Document

10.1007/s00605-011-0372-7

Cite this

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title = "Exponential sums with coefficients of certain Dirichlet series",

abstract = "Under the generalized Lindel{\"o}f Hypothesis in the t- and q-aspects, we bound exponential sums with coefficients of Dirichlet series belonging to a certain class. We use these estimates to establish a conditional result on squares of Hecke eigenvalues at Piatetski–Shapiro primes.",

keywords = "Exponential sums, Dirichlet series, Hecke eigenvalues, Piatetski–Shapiro primes",

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AB - Under the generalized Lindelöf Hypothesis in the t- and q-aspects, we bound exponential sums with coefficients of Dirichlet series belonging to a certain class. We use these estimates to establish a conditional result on squares of Hecke eigenvalues at Piatetski–Shapiro primes.

KW - Exponential sums

KW - Dirichlet series

KW - Hecke eigenvalues

KW - Piatetski–Shapiro primes

U2 - 10.1007/s00605-011-0372-7

DO - 10.1007/s00605-011-0372-7

M3 - Article

VL - 169

SP - 127

EP - 143

JO - Monatshefte für Mathematik

JF - Monatshefte für Mathematik

SN - 0026-9255

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