IDENTITIES INVOLVING COEFFICIENTS OF AUTOMORPHIC L-FUNCTIONS


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Abstract

Let f(z) be a holomorphic Hecke eigenform of weight k with respect to SL(2, ℤ) and let L(s,sym2 f) = ∑n=1 Cnn−sm Res>1 denote the symmetric square L-function of f. A Voronoi type formula for C(x)=∑n≥x cn and the relation C(x) = Ω±(x) are proved. Heuristic approaches to estimation of exponential sums arising in this connection are considered. Bibliography: 9 titles.

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