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

Published online by Cambridge University Press:  18 July 2011

CLAUDIA ALFES ,
KATHRIN BRINGMANN  and
JEREMY LOVEJOY
CLAUDIA ALFES
Affiliation:
Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstrasse 7, 64289 Darmstadt, Germany. e-mail: alfes@mathematik.tu-darmstadt.de
KATHRIN BRINGMANN
Affiliation:
Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany. e-mail: kbringma@math.uni-koeln.de
JEREMY LOVEJOY
Affiliation:
CNRS, LIAFA, Université Denis Diderot, Case 7014, 75205 Paris Cedex 13, France. e-mail: lovejoy@liafa.jussieu.fr
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Abstract

We define two-parameter generalizations of Andrews' (k+1)-marked odd Durfee symbols and 2kth symmetrized odd rank moments, and study the automorphic properties of some of their generating functions. When k = 0 we obtain families of modular forms and mock modular forms. When k ≥ 1, we find quasimodular forms and quasimock modular forms.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 151 , Issue 3 , November 2011 , pp. 385 - 406
Copyright
Copyright © Cambridge Philosophical Society 2011

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