Torus period coefficients on PGL(2) and Dirichlet series

Andre Reznikov

doi:10.1016/j.jnt.2012.07.013

Torus period coefficients on PGL(2) and Dirichlet series

Andre Reznikov

Department of Mathematics

Bar-Ilan University

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

Abstract

We fix a quadratic number field E, and the corresponding torus in PGL(2). We consider twisted (by a Hecke character of the field E) torus periods of automorphic functions. We prove meromorphic continuation for a Dirichlet series generated by these twisted periods.

Original language	English
Pages (from-to)	328-342
Number of pages	15
Journal	Journal of Number Theory
Volume	133
Issue number	1
DOIs	https://doi.org/10.1016/j.jnt.2012.07.013
State	Published - Jan 2013

Keywords

Double Dirichlet series
Hecke L-functions
Meromorphic continuation
Torus periods of cusp forms

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jnt.2012.07.013

Cite this

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title = "Torus period coefficients on PGL(2) and Dirichlet series",

abstract = "We fix a quadratic number field E, and the corresponding torus in PGL(2). We consider twisted (by a Hecke character of the field E) torus periods of automorphic functions. We prove meromorphic continuation for a Dirichlet series generated by these twisted periods.",

keywords = "Double Dirichlet series, Hecke L-functions, Meromorphic continuation, Torus periods of cusp forms",

author = "Andre Reznikov",

note = "Funding Information: ✩ Partially supported by the Veblen Fund at IAS, by the BSF grant 2006254, by the ISF Center of Excellency grant 1691/10, by the Minerva Center at ENI, and by the ERC grant 291612. E-mail address: [email protected].",

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AU - Reznikov, Andre

N1 - Funding Information: ✩ Partially supported by the Veblen Fund at IAS, by the BSF grant 2006254, by the ISF Center of Excellency grant 1691/10, by the Minerva Center at ENI, and by the ERC grant 291612. E-mail address: [email protected].

PY - 2013/1

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N2 - We fix a quadratic number field E, and the corresponding torus in PGL(2). We consider twisted (by a Hecke character of the field E) torus periods of automorphic functions. We prove meromorphic continuation for a Dirichlet series generated by these twisted periods.

AB - We fix a quadratic number field E, and the corresponding torus in PGL(2). We consider twisted (by a Hecke character of the field E) torus periods of automorphic functions. We prove meromorphic continuation for a Dirichlet series generated by these twisted periods.

KW - Double Dirichlet series

KW - Hecke L-functions

KW - Meromorphic continuation

KW - Torus periods of cusp forms

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U2 - 10.1016/j.jnt.2012.07.013

DO - 10.1016/j.jnt.2012.07.013

M3 - مقالة

SN - 0022-314X

VL - 133

SP - 328

EP - 342

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 1

ER -

Torus period coefficients on PGL(2) and Dirichlet series

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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