Number Theory Seminar

In this talk, I will introduce a family of integrals which represent the product of Rankin-Selberg L-functions of GL(l)xGL(m) and of GL(l)xGL(n) where m+n<l. When n=0, these integrals are those defined by Jacquet--Piatetski-Shapiro--Shalika up to a shift. As an application, we obtain a new proof of Jacquet's local converse conjecture using these new integrals and Cogdell--Shahidi--Tsai's theory on partial Bessel functions. This is joint work with Qing Zhang.