3 papers
math.NT2026
Some new modular Nahm sums of ranks 3 and 4
Zhineng Cao, Liuquan Wang
We discover six new families of modular Nahm sums in ranks 3 and 4. Two of them are rank three sums obtained by modifying two of Zagier's rank three examples. Three rank four famil…
math.NT2025
Some New Modular Rank Four Nahm Sums as Lift-dual of Rank Three Examples
Zhineng Cao, Liuquan Wang
We find nine new sets of rank four Nahm sums associated with nine different numeric matrices which are likely to be modular. They are discovered by applying the lift-dual operation…
math.NT2024
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…