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)|
|Number of pages||30|
|Journal||Journal of the Institute of Mathematics of Jussieu|
|State||Published - Jan 2010|
Bibliographical noteFunding 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.
- Eisenstein series
- Integral moments
- Meromorphic continuation
- Poincaré series
- Spectral decomposition