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On the central value of symmetric square L-functions

Authors:	Valentin Blomer

Institution:	(1) Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, ON, Canada, M5S 2E4

Abstract:	Let S _k(N, χ) be the space of cusp forms of weight k, level N and character χ. For $f \in S_k(N, \chi)$ let L(s, sym² f) be the symmetric square L-function and $L(s, f \otimes f)$ be the Rankin–Selberg square attached to f. For fixed k ≥ 2, N prime, and real primitive χ, asymptotic formulas for the first and second moment of the central value of L(s, sym² f) and $L(s, f \otimes f)$ over a basis of S _k(N, χ) are given as N → ∞. As an application it is shown that a positive proportion of the central values L(1/2, sym² f) does not vanish. The author was supported by NSERC grant 311664-05.

Keywords:	Symmetric square L-function Nonvanishing Mollification Central value Rankin– Selberg L-function
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