Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function

Scott Ahlgren, Nickolas Andersen

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Abstract

We construct a natural basis for the space of weak harmonic Maass forms of weight 5/2 on the full modular group. The nonholomorphic part of the first element of this basis encodes the values of the ordinary partition function p(n). We obtain a formula for the coefficients of the mock modular forms of weight 5/2 in terms of regularized inner products of weakly holomorphic modular forms of weight −1/2, and we obtain Hecke-type relations among these mock modular forms.

Original languageEnglish (US)
Article number10
JournalResearch in Number Theory
Volume1
Issue number1
DOIs
StatePublished - Dec 1 2015

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ASJC Scopus subject areas

  • Algebra and Number Theory

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