Regularized inner products of modular functions

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.

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Bibliographic Details
Published in:The Ramanujan journal 2016-11, Vol.41 (1-3), p.13-29
Main Authors: Duke, W., Imamoḡlu, Ö., Tóth, Á.
Format: Article
Language:English
Subjects:
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
Regularization
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Description
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.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-013-9544-5