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arXiv · 2507.20270

Proofs of Two Conjectural Identities on Partial Nahm Sums

Changsong Shi·Liuquan Wang
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Abstract

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 conjecture consisting of two Rogers--Ramanujan type identities for the remaining family. We prove these conjectural identities in two steps. First, employing a transformation formula involving two Bailey pairs, we transform the partial Nahm sums into some specific Hecke-type series. Second, using two distinct approaches, we convert these Hecke-type series to the desired modular infinite products.

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Changsong Shi, Liuquan Wang. 2025-07-27. Proofs of Two Conjectural Identities on Partial Nahm Sums. https://arxiv.org/abs/2507.20270

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