Determination of GL(3) cusp forms by central values of GL(3) x GL(2) L-functions, level aspect

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 L(1/2, f x h) = L(1/2, g x h) for all h is an element of S-10*(q), for infinitely many primes q, then f = g. (C) 2011 Elsevier Inc. All rights reserved.