3 papers
math.NT2026
Nahm Sums Dual to Zagier's Rank-Three Examples and Related Identities
Changsong Shi, Liuquan Wang
In 2007, Zagier identified twelve families of candidates for rank-three modular Nahm sums and established the modularity of three of them. The remaining cases were subsequently con…
math.NT2025
Proofs of Two Conjectural Identities on Partial Nahm Sums
Changsong Shi, Liuquan Wang
Recently, Wang and Zeng investigated modularity of partial Nahm sums and discovered 14 modular families of such sums. They confirmed modularity for 13 families and proposed a conje…
math.NT2025
Modularity of tadpole Nahm sums in ranks 4 and 5
Changsong Shi, Liuquan Wang
Around 2016, Calinescu, Milas and Penn conjectured that the rank Nahm sum associated with the tadpole Cartan matrix is modular, and they provided a proof for .…