IDENTITIES INVOLVING COEFFICIENTS OF AUTOMORPHIC L-FUNCTIONS

摘要

Let f(z) be a holomorphic Hecke eigenform of weight k with respect to SL(2, Z) and let L(s,sym~2 f) = ∑ from n = 1 to ∞ of c_nn~(-s), Re s > 1, denote the symmetric square L-function of f. A Voronoi type formula for C(x) = ∑_(n ≤ x)c_n and the relation C(x) = Ω_± (x~(1/3)) are proved. Heuristic approaches to estimation of exponential sums arising in this connection are considered.