n-COLOR OVERPARTITIONS, TWISTED DIVISOR FUNCTIONS, AND ROGERS-RAMANUJAN IDENTITIES

Print ISSN: 0972-7752

Abstract

In the early 90’s Andrews discussed a certain q-series whose coefficients are determined by a twisted divisor function. We provide several other examples of this nature. All of these q-series can be interpreted combinatorially in terms of n-color overpartitions, as can some closely related series occurring in identities of the Rogers-Ramanujan type.

Keywords and Phrases

Partitions, overpartitions, n-color overpartitions, real quadratic fields, Bailey pairs, Rogers-Ramanujan identities.

A.M.S. subject classification

11P81, 05A17, 33D15.

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