Riemann's Zeta Function and Beyond

Details Riemann's Zeta Function and Beyond Riemann's Zeta Function and Beyond

2003-09-30

arxiv.org/abs/math/0309478v1

Mathematics

Number Theory

Survey, 63 pages, to appear in the Bulletin of the A.M.S., 2004

Scientific paper

In recent years L-functions and their analytic properties have assumed a central role in number theory and automorphic forms. In this expository article, we describe the two major methods for proving the analytic continuation and functional equations of $L$-functions: the method of integral representations, and the method of Fourier expansions of Eisenstein series. Special attention is paid to technical properties, such as boundedness in vertical strips; these are essential in applying the converse theorem, a powerful tool that uses analytic properties of L-functions to establish cases of Langlands functoriality conjectures. We conclude by describing striking recent results which rest upon the analytic properties of L-functions.

Affiliated with

Also associated with

No associations

Rating

Riemann's Zeta Function and Beyond 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 Riemann's Zeta Function and Beyond, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Riemann's Zeta Function and Beyond will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-280281