6 papers · 1 filter
Modularity of Some Nahm Sums as Vector-valued Functions
Liuquan Wang, Huohong Zhang
Zagier observed that modular Nahm sums associated with the same matrix may form a vector-valued modular function on some congruence subgroup. We establish modular transformation fo…
Some New Modular Rank Three Nahm Sums from a Lift-Dual Operation
Zhineng Cao, Liuquan Wang
Around 2007, Zagier discovered some rank two and rank three Nahm sums, and their modularity have now all been confirmed. Zagier also observed that the dual of a modular Nahm sum is…
Counterexamples to Zagier's Duality Conjecture on Nahm Sums
Liuquan Wang
Given any positive integer , Nahm's problem is to determine all rational positive definite matrix , -dimensional rational vector and rational scalar su…
Proofs of Mizuno's Conjectures on Rank Three Nahm Sums of Index
Boxue Wang, Liuquan Wang
Mizuno provided 15 examples of generalized rank three Nahm sums with symmetrizer which are conjecturally modular. Using the theory of Bailey pairs and some $…
Mizuno's rank three Nahm sums I: identities of index
Boxue Wang, Liuquan Wang
Mizuno provided 19 examples of generalized rank three Nahm sums with symmetrizer which are conjecturally modular. We confirm their modularity by establishing…
Leading coefficient in the Hankel determinants related to binomial and -binomial transforms
Shane Chern, Lin Jiu, Shuhan Li +1
It is a standard result that the Hankel determinants for a sequence stay invariant after performing the binomial transform on this sequence. In this work, we extend the scenario to…