arXiv subjects
Publications and source records attributed to Alexei Pantchichkine.
We introduce an analog of part of the Langlands-Shahidi method to the p-adic setting, constructing reciprocals of certain p-adic L-functions using the nonconstant terms of the Fourier expansions of Eisenstein series. We carry out the method for the group SL(2), and give explicit p-adic measures whose Mellin transforms are reciprocals of Dirichlet L-functions.
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