p-adic L-functions for GSp(4) x GL (2).

[摘要] Let p be an odd prime.In this thesis we constructa p-adic analog of a degree eight L-function L(s,Fxf) where F is an ordinaryholomorphic degree 2 Siegel eigen cusp form oflevel 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-adicallyinterpolates the L-valuesas 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.

[发布机构] University of Michigan

[效力级别] Siegel Modular Forms

[关键词] P-adic L-function;Siegel Modular Forms;Pullback;Interpolate;Mathematics;Science;Mathematics