Guardat en:
| Autor principal: | |
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| Format: | Preprint |
| Publicat: |
2001
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| Matèries: | |
| Accés en línia: | https://arxiv.org/abs/math/0111312 |
| Etiquetes: |
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Taula de continguts:
- We prove an approximate functional equation for the central value of the L-series attached to an irreducible cuspidal automorphic representation of GL(m) over a number field with unitary central character. We investigate the decay rate of the terms involved using the analytic conductor of Iwaniec and Sarnak as a guideline. Straightforward extensions of the results exist for products of central values. We hope that these formulae will help further understanding of the central values of principal L-functions, such as finding good bounds on their various power means, or establishing subconvexity or nonvanishing results in certain families. A crucial role in the proofs is played by recent progress on the Ramanujan--Selberg conjectures achieved by Luo, Rudnick and Sarnak. The bounds at the non-Archimedean places enter through the work of Molteni.