Multiple Dirichlet series and shifted convolutions

Jeff Hoffstein; Thomas A. Hulse; Andre Reznikov

doi:10.1016/j.jnt.2015.10.001

Multiple Dirichlet series and shifted convolutions

Jeff Hoffstein, Thomas A. Hulse, Andre Reznikov

Department of Mathematics

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

17 Scopus citations

Abstract

We define, and obtain the meromorphic continuation of, shifted Rankin-Selberg convolutions in one and two variables. As sample applications, this continuation is used to obtain estimates for single and double shifted sums and a Burgess-type bound for L-series associated to modular forms of arbitrary central character. Further applications are furnished by subsequent works by the authors and their colleagues.

Original language	English
Pages (from-to)	457-533
Number of pages	77
Journal	Journal of Number Theory
Volume	161
DOIs	https://doi.org/10.1016/j.jnt.2015.10.001
State	Published - 2016

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc.

Keywords

L-functions of automorphic forms
Second moments
Shifted convolutions
Subconvexity bounds

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10.1016/j.jnt.2015.10.001

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AU - Reznikov, Andre

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AB - We define, and obtain the meromorphic continuation of, shifted Rankin-Selberg convolutions in one and two variables. As sample applications, this continuation is used to obtain estimates for single and double shifted sums and a Burgess-type bound for L-series associated to modular forms of arbitrary central character. Further applications are furnished by subsequent works by the authors and their colleagues.

KW - L-functions of automorphic forms

KW - Second moments

KW - Shifted convolutions

KW - Subconvexity bounds

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JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Multiple Dirichlet series and shifted convolutions

Abstract

Bibliographical note

Keywords

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