Harmonic Maass forms and periods

Published 7 Nov 2011 in math.NT and math.AG | (1111.1508v1)

Abstract: According to Waldspurger's theorem, the coefficients of half-integral weight eigenforms are given by central critical values of twisted Hecke L-functions, and therefore by periods. Here we prove that the coefficients of weight 1/2 harmonic Maass forms are determined by periods of algebraic differentials of the third kind on modular and elliptic curves.

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Jan Hendrik Bruinier

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