Uniform approximate functional equation for principal L-functions
Uniform approximate functional equation for principal L-functions
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DOI：
10.1155/s1073792802111184
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发表时间：
2001-11
影响因子：
1
通讯作者：
G. Harcos
中科院分区：
文献类型：
--
作者：
G. Harcos
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.
