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Mock theta functions, ranks, and Maass forms. (English) Zbl 1183.11064
Alladi, Krishnaswami (ed.), Surveys in number theory. New York, NY: Springer (ISBN 978-0-387-78509-7/hbk). Developments in Mathematics 17, 119-141 (2008).
Summary: This paper is a survey of some recent joint work with {\it K. Bringmann} [Dyson’s ranks and Maass forms, Ann. Math. (2), accepted for publication] on harmonic weak Maass forms. We summarize applications to Dyson’s rank-partition statistic and the conjecture of Andrews and Dragonette on Ramanujan’s third-order mock theta function $f(q)$. For the entire collection see [Zbl 1147.11004].
11P82Analytic theory of partitions
11P83Partitions: congruences and congruential restrictions
11F46Siegel modular groups and their modular and automorphic forms
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