On Some Double Nahm Sums of Zagier
Number Theory
2023-03-03 v1 Combinatorics
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 -series proof for the tenth example. We prove that the fifth and the tenth examples are in fact equivalent. Then we give a -series proof for the fifth example, which confirms a recent conjecture of Wang. This also serves as the first -series proof for the tenth example, whose explicit form was conjectured by Vlasenko and Zwegers in 2011.
Keywords
Cite
@article{arxiv.2303.01333,
title = {On Some Double Nahm Sums of Zagier},
author = {Zhineng Cao and Hjalmar Rosengren and Liuquan Wang},
journal= {arXiv preprint arXiv:2303.01333},
year = {2023}
}
Comments
9 pages