Uniform approximate functional equation for principal L-functions

Details Uniform approximate functional equation for principal L-functions Uniform approximate functional equation for principal L-functions

2001-11-30

arxiv.org/abs/math/0111312v3

Int. Math. Res. Not. 2002, no. 18, 923-932

Mathematics

Number Theory

8 pages, LaTeX2e; v2: shorter abstract in paper, recent amsart package used; v3: small alterations in the text (most important

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Uniform approximate functional equation for principal L-functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Uniform approximate functional equation for principal L-functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Uniform approximate functional equation for principal L-functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-577879