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 the holomorphic parts 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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Notes
For brevity we will often drop the attribute “weak” in this paper.
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The author is partially supported by DFG Grant BR-2163/2-2.