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,fχ) 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