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Regularized inner products of modular functions. (English) Zbl 1418.11069
Summary: In this note, we give an explicit basis for the harmonic weak forms of weight two. We also show that their holomorphic coefficients can be given in terms of regularized inner products of weight zero weakly holomorphic forms.

11F12 Automorphic forms, one variable
11F30 Fourier coefficients of automorphic forms
11F41 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
Full Text: DOI
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