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math.NT2022
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…
math.NT2022
Multi-sum Rogers-Ramanujan Type Identities
Zhineng Cao, Liuquan Wang
We use an integral method to establish a number of Rogers-Ramanujan type identities involving double and triple sums. The key step for proving such identities is to find some infin…
math.CO2022
New Proofs of Some Double Sum Rogers-Ramanujan Type Identities
Liuquan Wang
Recently, Rosengren utilized an integral method to prove a number of conjectural identities found by Kanade and Russell. Using this integral method, we give new proofs to some doub…