Shunsuke Yamana (Kyushu University)
L-functions and theta correspondence

The doubling method of Piatetski-Shapiro and Rallis applies in the local situation to define local factors of representations of classical groups. On the one hand, the L-factor is defined as a g.c.d. of the local zeta integrals for all good sections. On the other hand, it is defined from the gamma factor by using the Langlands classification. In this talk I develop a theory of the zeta integral and prove that the two candidates of the L-factor agree. Applications include a characterization of nonvanishing of global theta liftings in terms of the analytic properties of the complete L-functions and the occurrence in the local theta correspondence. My paper is available on line: DOI 10.1007/s00222-013-0476-x