Journal of the Institute of Mathematics of Jussieu

Table of Contents - 2010 - Volume 9, Issue 01  

Cambridge Journals Online - CUP Full-Text Page
Journal of the Institute of Mathematics of Jussieu (2010), 9:95-124 Cambridge University Press
Copyright © Cambridge University Press 2010
doi:10.1017/S1474748009000188

Research Article

Subconvexity bounds for automorphic L-functions

A. Diaconua1 and P. Garretta2

a1 School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA (cad@math.umn.edu)
a2 School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA (garrett@math.umn.edu)
Article author query
diaconu a [Google Scholar]
garrett p [Google Scholar]

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,fxs2297χ) by Grossencharacters χ, from our previous paper on integral moments.

(Received March 27 2008)

(Revised April 16 2009)

(Accepted April 16 2009)

Keywordssubconvexity; L-functions; integral moments; Poincaré series; Eisenstein series; spectral decomposition; meromorphic continuation

AMS 2000 Mathematics subject classificationPriamry 11R42; Secondary 11F66; 11F67; 11F70; 11M41; 11R47