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- W2963557378 abstract "In Ramanujan’s final letter to Hardy, he listed examples of a strange new class of infinite series he called “mock theta functions”. It turns out all of these examples are essentially specializations of a so-called universal mock theta function [Formula: see text] of Gordon–McIntosh. Here we show that [Formula: see text] arises naturally from the reciprocal of the classical Jacobi triple product—and is intimately tied to rank generating functions for unimodal sequences, which are connected to mock modular and quantum modular forms—under the action of an operator related to statistical physics and partition theory, the [Formula: see text]-bracket of Bloch–Okounkov. Second, we find [Formula: see text] to extend in [Formula: see text] to the entire complex plane minus the unit circle, and give a finite formula for this universal mock theta function at roots of unity, that is simple by comparison to other such formulas in the literature; we also indicate similar formulas for other [Formula: see text]-hypergeometric series. Finally, we look at interesting “quantum” behaviors of mock theta functions inside, outside, and on the unit circle." @default.
- W2963557378 created "2019-07-30" @default.
- W2963557378 creator A5035269354 @default.
- W2963557378 date "2018-07-23" @default.
- W2963557378 modified "2023-10-16" @default.
- W2963557378 title "Jacobi’s triple product, mock theta functions, unimodal sequences and the q-bracket" @default.
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- W2963557378 doi "https://doi.org/10.1142/s1793042118501178" @default.
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