Bailey-pair methods yield floor((r+4)/2) modular Nahm sums for C(D_r)^{-1}, confirming Sun–Wang’s zero-vector identity and partial companions.
Some New Modular Rank Three Nahm Sums from a Lift-Dual Operation
3 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
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 likely to be modular. This duality observation motivates us to discover some new modular rank three Nahm sums by a lift-dual operation. We first lift Zagier's rank two Nahm sums to rank three and then calculate their dual, and we show that these dual Nahm sums are indeed modular. We achieve this by establishing the corresponding Rogers--Ramanujan type identities, which express these Nahm sums as modular infinite products.
fields
math.NT 3years
2026 3representative citing papers
Four previously conjectural modular rank-four Nahm-sum identities are proved by q-series reductions, and two further conjectures are shown to imply each other.
Six new families of modular Nahm sums of ranks 3 and 4 are found and shown to equal modular infinite products via Rogers-Ramanujan identities.
citing papers explorer
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Modular Nahm Sums for the Inverse Cartan Matrix of Type $D_r$
Bailey-pair methods yield floor((r+4)/2) modular Nahm sums for C(D_r)^{-1}, confirming Sun–Wang’s zero-vector identity and partial companions.
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Proofs of five conjectural identities on modular rank four Nahm sums
Four previously conjectural modular rank-four Nahm-sum identities are proved by q-series reductions, and two further conjectures are shown to imply each other.
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Some new modular Nahm sums of ranks 3 and 4
Six new families of modular Nahm sums of ranks 3 and 4 are found and shown to equal modular infinite products via Rogers-Ramanujan identities.