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Proofs of Mizuno's Conjectures on Generalized Rank Two Nahm Sums
Boxue Wang, Liuquan Wang
Recently, Mizuno studied generalized Nahm sums associated with symmetrizable matrices. He provided 14 sets of candidates of modular Nahm sums in rank two and justified four of them…
On Some Double Nahm Sums of Zagier
Zhineng Cao, Hjalmar Rosengren, Liuquan Wang
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 pro…
Explicit Forms and Proofs of Zagier's Rank Three Examples for Nahm's Problem
Liuquan Wang
Let be a positive integer, a real positive semi-definite symmetric rational matrix, a rational vector of length , and a rational scalar. Nahm's…
Modular Proofs of Gosper's Identities
Liuquan Wang
We give unified modular proofs to all of Gosper's identities on the -constant . We also confirm Gosper's observation that for any distinct positive integers $n_1,\cdots,n_m…
Sign Changes of Coefficients of Powers of the Infinite Borwein Product
Liuquan Wang
We denote by the coefficient of in the series expansion of , which is the -th power of the infinite Borwein product. Le…
A Family of Supercongruences Involving Multiple Harmonic Sums
Megan McCoy, Kevin Thielen, Liuquan Wang +1
In recent years, the congruence first discovered by the last author have been generalized by eithe…