Analytic constructions of p-adic L-functions and Eisenstein series

Details Analytic constructions of p-adic L-functions and Eisenstein series Analytic constructions of p-adic L-functions and Eisenstein series

2012-04-17

arxiv.org/abs/1204.3878v1

Mathematics

Number Theory

38 pages, including the Appendix "On p-adic L-functions for GSp(4)" on a joint work with I.I. Piatetski-Shapiro (IAS, 1999)

Scientific paper

The Fourier coefficients of the Siegel-Eisenstein series are p-adically continued for all primes p, as meromorphic functions, using the reciprocal of a product of L-functions. A construction of p-adic meromorphic families of such series is given in relation to the geometry of homogeneous spaces. Applications are given to p-adic L-functions, to Siegel's Mass Formula, to p-adic analytic families of automorphic representations. Based on author's talk for the Conference Automorphic Forms and Related Geometry, Assessing the Legacy of I.I. Piatetski-Shapiro

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