Determination of GL(3) Cusp Forms by Central Values of GL(3) x GL(2) L-functions

Abstract

Let f be a self-dual Hecke-Maass cusp form for GL(3). We show that f is uniquely determined by central values of GL(2) twists of its L-function. More precisely, if g is another self-dual GL(3) Hecke-Maass cusp form such that for all holomorphic Hecke eigenforms for all k ≡ 0 (mod 4), then f = g.