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arXiv · 2303.01333

On Some Double Nahm Sums of Zagier

Zhineng Cao·Hjalmar Rosengren·Liuquan Wang
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Abstract

Zagier provided eleven conjectural rank two examples for Nahm's problem. All of them have been proved in the literature except for the fifth example, and there is no $q$-series proof for the tenth example. We prove that the fifth and the tenth examples are in fact equivalent. Then we give a $q$-series proof for the fifth example, which confirms a recent conjecture of Wang. This also serves as the first $q$-series proof for the tenth example, whose explicit form was conjectured by Vlasenko and Zwegers in 2011.

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Zhineng Cao, Hjalmar Rosengren, Liuquan Wang. 2023-03-02. On Some Double Nahm Sums of Zagier. https://arxiv.org/abs/2303.01333

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