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Fourier coefficients of polyharmonic Maass forms

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Toshiki Matsusaka
Kyushu University/University of Cologne
Wed, 2018-05-16 14:30 - 15:30
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Lagarias and Rhoades introduced a new class called polyharmonic Maass forms, which are a generalization of harmonic Maass forms. They gave a standard basis for the space of such forms by means of the higher Laurent coefficients of real analytic Eisenstein series. In this talk, we consider a large space of polyharmonic weak Maass forms of integral or half-integral weight, and construct a basis for this space. Furthermore, as an analogue of Zagier’s work on traces of singular moduli, we express the Fourier coefficients in terms of traces of CM-values and cycle integrals.

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