ON THE NONVANISHING OF THE CENTRAL VALUE OF THE RANKIN-SELBERG L-FUNCTIONS

摘要

Let π_1 and π_2 be irreducible unitary cuspidal automorphic representations of GL_m(A) and GL_n(A), respectively, where A is the ring of adeles attached to a number field k. The basic analytic properties (meromorphic continuation and the functional equation) of the Rankin-Selberg L-functions L(s,π_1 * π_2) have been established through the work [JPSS83], [CPS04] and also [Shd88] and [MW89], It is known from [Shd84] that the L-functions L(S,π_1 * π_2) defined by the Rankin-Selberg method and by the Langlands-Shahidi method are the same.