Non-vanishing of periods of automorphic functions

Andre Reznikov

doi:10.1515/form.2001.018

Non-vanishing of periods of automorphic functions

Andre Reznikov

Weizmann Institute of Science

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Abstract

We study a period defined for three automorphic functions on GL(2). We give a lower bound on the average size of such a period which is essentially sharp. We deduce from this bound a non-vanishing result for this period. As an application we obtain non-vanishing of certain L-functions at 1/2.

Original language	English
Pages (from-to)	485-493
Number of pages	9
Journal	Forum Mathematicum
Volume	13
Issue number	4
DOIs	https://doi.org/10.1515/form.2001.018
State	Published - 2001
Externally published	Yes

Bibliographical note

Funding Information:
This work was supported in part by BSF grant No. 94-00312/2 and by the ECTMR network ``Algebraic Lie Representations'' – ERB FMRX-CT97-0100.

Funding

This work was supported in part by BSF grant No. 94-00312/2 and by the ECTMR network ``Algebraic Lie Representations'' – ERB FMRX-CT97-0100.

Funders	Funder number
United States-Israel Binational Science Foundation	ERB FMRX-CT97-0100, 94-00312/2

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10.1515/form.2001.018

Cite this

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abstract = "We study a period defined for three automorphic functions on GL(2). We give a lower bound on the average size of such a period which is essentially sharp. We deduce from this bound a non-vanishing result for this period. As an application we obtain non-vanishing of certain L-functions at 1/2.",

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AB - We study a period defined for three automorphic functions on GL(2). We give a lower bound on the average size of such a period which is essentially sharp. We deduce from this bound a non-vanishing result for this period. As an application we obtain non-vanishing of certain L-functions at 1/2.

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Non-vanishing of periods of automorphic functions

Abstract

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