Modularity of tadpole Nahm sums in ranks 4 and 5.
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| Title: | Modularity of tadpole Nahm sums in ranks 4 and 5. |
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| Authors: | Shi, Changsong1 (AUTHOR) changsong@whu.edu.cn, Wang, Liuquan1 (AUTHOR) mathlqwang@163.com |
| Source: | Journal of Number Theory. Jul2026, Vol. 284, p214-245. 32p. |
| Subjects: | Modular forms, Theta functions, Mathematical formulas |
| Abstract: | Around 2016, Calinescu, Milas and Penn conjectured that the rank r Nahm sum associated with the r × r tadpole Cartan matrix is modular, and they provided a proof for r = 2. The r = 3 case was recently resolved by Milas and Wang. We prove this conjecture for the next cases r = 4 , 5. We also prove the modularity of some companion Nahm sums by establishing the corresponding Rogers–Ramanujan type identities. A key new ingredient in our proofs is some rank reduction formulas which allow us to decompose higher rank tadpole Nahm sums to mixed products of some lower rank Nahm-type sums and theta functions. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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