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Artigo Acesso aberto Revisado por pares
BIBTEX RIS

Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms

2013; Elsevier BV; Volume: 246; Linguagem: Inglês

10.1016/j.aim.2013.05.028

ISSN

1090-2082

Autores

Jan Hendrik Bruinier, Ken Ono,

Tópico(s)

Advanced Algebra and Geometry

Resumo

We prove that the coefficients of certain weight −1/2 harmonic Maass forms are "traces" of singular moduli for weak Maass forms. To prove this theorem, we construct a theta lift from spaces of weight −2 harmonic weak Maass forms to spaces of weight −1/2 vector-valued harmonic weak Maass forms on Mp2(Z), a result which is of independent interest. We then prove a general theorem which guarantees (with bounded denominator) when such Maass singular moduli are algebraic. As an example of these results, we derive a formula for the partition function p(n) as a finite sum of algebraic numbers which lie in the usual discriminant −24n+1 ring class field.

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