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

Alexei Pantchichkine (1)

1 IF - Institut Fourier

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

Mots clés: Siegel-Eisenstein series; p-adic L-functions; pseudomeasures; reciprocal of L-functions; families of automorphic representations

Domaines: Théorie des nombres [math.NT]

Alexei Pantchichkine. Analytic constructions of p-adic L-functions and Eisenstein series. Contemporary mathematics, 2014, 614, pp.345-374. ⟨hal-00688525⟩