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 | |
| 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