Generalized rank deviations for overpartitions
Kevin Allen, Robert Osburn, Matthias Storzer
TL;DR
This paper derives formulas for generalized rank deviations in overpartitions using Appell-Lerch series and theta functions, extending previous work and providing a dissection as an application.
Contribution
It introduces new formulas for rank deviations in overpartitions expressed through Appell-Lerch series and theta functions, extending prior research.
Findings
Formulas for generalized rank deviations in overpartitions
Expressions in terms of Appell-Lerch series and theta functions
Computed a dissection as an application
Abstract
We prove formulas for generalized rank deviations for overpartitions. These formulas are in terms of Appell-Lerch series and sums of quotients of theta functions and extend work of Lovejoy and the second author. As an application, we compute a dissection.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry