Determination of GL(3) cusp forms by central values of GL(3)×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(12,f×h)=L(12,g×h) for all h∈S10⁎(q), for infinitely many primes q, then f=g.