Overpartitions and class numbers of binary quadratic forms

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We show that the Zagier-Eisenstein series shares its non-holomorphic part with certain weak Maass forms whose holomorphic parts are generating functions for overpartition rank differences. This has a number of consequences, including exact formulas, asymptotics, and congruences for the rank differences as well as $q$-series identities of the mock theta type.
9 pages

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Number Theory, Combinatorics

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http://salesiana.dossiersoluciones.com/handle/123456789/143581

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0712.0631
 http://arxiv.org/abs/0712.0631

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arXiv