p-adic L-functions for GSp(4)xGL(2)
by
Mahesh Agarwal
McMaster University

Let p be an odd prime. In this talk we will construct a p-adic analog of a degree eight L-function

L(s, F×f) where F is an ordinary holomorphic degree 2 Siegel eigen cusp form of level a power of

p and f is an ordinary eigen cusp form of level a power of p.

Our method makes use of the work of M. Furusawa which gives an integral representation

for this L-function. By suitably interpreting this integral representation in the context of

inner products of automorphic forms, we show that it p-adically interpolates the

L-values as the forms F and f vary in ordinary families (with the weights varying p-adically).

This interpolation is carried out by constructing an Eisenstein measure on a

higher-rank unitary group and exploiting a pull-back formula of P. Garrett and G. Shimura

to get a new Integral representation of the degree 8 L-function.

Date received: April 10, 2008