Lei Zhang (Boston College)
Tensor Product L-functions of Quasi-split Classical Groups of Hermitian Type.

Recently, we established a family of global zeta integrals representing a product of tensor product (partial) L-functions of a quasi-split classical group of Hermitian type and general linear group. The cuspidal automorphic representations of the classical group are possibly non-generic. We mainly use the Bessel coefficients of automorphic forms to construct this global zeta integrals and generalize the results of Ginzburg, Piatetski-Shapiro and Rallis in 1997 on orthogonal group cases. We prove that the global integrals are eulerian and finish the explicit calculation of unramified local zeta integrals in a certain case, which is enough to represent the product of unramified tensor product local $L$-functions. Moreover, we will use the local zeta integrals to define the local factors.