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arXiv · 1812.02922

Dissections of strange $q$-series

Scott Ahlgren·Byungchan Kim·Jeremy Lovejoy
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Abstract

In a study of congruences for the Fishburn numbers, Andrews and Sellers observed empirically that certain polynomials appearing in the dissections of the partial sums of the Kontsevich-Zagier series are divisible by a certain $q$-factorial. This was proved by the first two authors. In this paper we extend this strong divisibility property to two generic families of $q$-hypergeometric series which, like the Kontsevich-Zagier series, agree asymptotically with partial theta functions.

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Scott Ahlgren, Byungchan Kim, Jeremy Lovejoy. 2018-12-07. Dissections of strange $q$-series. https://arxiv.org/abs/1812.02922

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