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Article Dans Une Revue International Mathematics Research Notices Année : 2010

Automorphic properties of generating functions for generalized rank moments and Durfee symbols

Résumé

We define two-parameter generalizations of two combinatorial constructions of Andrews: the kth symmetrized rank moment and the k-marked Durfee symbol. We prove that three specializations of the associated generating functions are so-called quasimock theta functions, while a fourth specialization gives quasimodular forms. We then define a two-parameter generalization of Andrews' smallest parts function and note that this leads to quasimock theta functions as well. The automorphic properties are deduced using q-series identities relating the relevant generating functions to known mock theta functions.

Dates et versions

hal-00409605 , version 1 (10-08-2009)

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Jeremy Lovejoy, Kathrin Bringmann, Robert Osburn. Automorphic properties of generating functions for generalized rank moments and Durfee symbols. International Mathematics Research Notices, 2010, 2, pp.238-260. ⟨10.1093/imrn/rnp131⟩. ⟨hal-00409605⟩
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