L-functions for GSp4

Integral representation for L-functions for GSp4 ×GL2, II

Based on Furusawa’s theory [7], we present an integral representation for the L-function L(s, π× τ), where π is a cuspidal automorphic representation on GSp4 related to a holomorphic Siegel modular form, and where τ is an arbitrary cuspidal automorphic representation on GL2. As an application, a special value result for this L-function in the spirit of Deligne’s conjecture is proved.

Bessel models and L-functions for the Steinberg representation of GSp4

We obtain explicit formulas for the test vector in the Bessel model and derive the criteria for existence and uniqueness for Bessel models for the unramified, quadratic twists of the Steinberg representation π of GSp4(F ), where F is a non-archimedean local field of characteristic zero. We also give precise criteria for the Iwahori spherical vector in π to be a test vector. We apply the formula...

SPECIAL VALUES OF L-FUNCTIONS ON GSp4×GL2 AND THE NON-VANISHING OF SELMER GROUPS

In this paper we show how one can use an inner product formula of Heim giving the inner product of a pullback Eisenstein series from Sp10 to Sp2×Sp4×Sp4 with a newform on GL2 and a SaitoKurokawa lift to produce congruences between Saito-Kurokawa lifts and non-CAP forms. This congruence is in part controlled by the L-function on GSp4×GL2. The congruence is then used to produce nontrivial torsion...

Geometric Bessel models for GSp4 and multiplicity one

0.1 In this paper, which is a sequel to [4], we study Bessel models of representations of GSp4 in the framework of the geometric Langlands program. These models introduced by Novodvorsky and Piatetski-Shapiro, satisfy the following multiplicity one property ([6]). Set k = Fq and O = k[[t]] ⊂ F = k((t)). Let F̃ be an étale F -algebra with dimF (F̃ ) = 2 such that k is algebraically closed in F̃ . W...

L-functions for Gsp 4