Subconvexity bounds for automorphic L-functions

A. Diaconu; P. Garrett

doi:10.1017/S1474748009000188

Subconvexity bounds for automorphic L-functions

A. Diaconu, P. Garrett

Mathematics

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

12 Scopus citations

Abstract

We break the convexity bound in the t-aspect for L-functions attached to cusp forms f for GL2(k) over arbitrary number fields k. The argument uses asymptotics with error term with a power saving, for second integral moments over spectral families of twists L(s,f⊗X) by Grossencharacters , from our previous paper on integral moments.

Original language	English (US)
Pages (from-to)	95-124
Number of pages	30
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	9
Issue number	1
DOIs	https://doi.org/10.1017/S1474748009000188
State	Published - Jan 2010

Bibliographical note

Funding Information:
Acknowledgements. Both authors were partially supported by NSF Grant DMS-0652488. We would like to acknowledge useful comments and advice from P. Sarnak. We also thank the anonymous referee for helpful comments and suggestions.

Keywords

Eisenstein series
Integral moments
L-functions
Meromorphic continuation
Poincaré series
Spectral decomposition
Subconvexity

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AB - We break the convexity bound in the t-aspect for L-functions attached to cusp forms f for GL2(k) over arbitrary number fields k. The argument uses asymptotics with error term with a power saving, for second integral moments over spectral families of twists L(s,f⊗X) by Grossencharacters , from our previous paper on integral moments.

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KW - Integral moments

KW - L-functions

KW - Meromorphic continuation

KW - Poincaré series

KW - Spectral decomposition

KW - Subconvexity

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Subconvexity bounds for automorphic L-functions

Abstract

Bibliographical note

Keywords

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