Lifting cusp forms to Maass forms with an application to partitions.

Abstract:

:For 2 < k [abstract: see text] we define lifts of cuspidal Poincaré series in S(k)(Gamma(0)(N)) to weight 2 - k harmonic weak Maass forms. This construction answers a question of Dyson by providing the general framework "explaining" Ramanujan's mock theta functions. As an application, we show that the number of partitions of a positive integer n is the "trace" of singular moduli of a Maass form arising from the lift of a weight 4 cusp form corresponding to a Calabi-Yau threefold.

authors

Bringmann K,Ono K

doi

10.1073/pnas.0611414104

subject

Has Abstract

pub_date

2007-03-06 00:00:00

pages

3725-31

issue

10

eissn

0027-8424

issn

1091-6490

pii

0611414104

journal_volume

104

pub_type

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