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Subconvexity bounds for automorphic L-functions

Part of: Zeta and $L$-functions: analytic theory Algebraic number theory: global fields Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  23 July 2009

A. Diaconu  and
P. Garrett
A. Diaconu
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA (cad@math.umn.edu)
P. Garrett
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA (garrett@math.umn.edu)
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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⊗χ) by Grossencharacters χ, from our previous paper on integral moments.

Keywords

subconvexityL-functionsintegral momentsPoincaré seriesEisenstein seriesspectral decompositionmeromorphic continuation

MSC classification

Secondary: 11R42: Zeta functions and $L$-functions of number fields 11F66: Langlands $L$-functions; one variable Dirichlet series and functional equations 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols 11F70: Representation-theoretic methods; automorphic representations over local and global fields 11M41: Other Dirichlet series and zeta functions 11R47: Other analytic theory
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 9 , Issue 1 , January 2010 , pp. 95 - 124
Copyright
Copyright © Cambridge University Press 2010

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