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math.NT2026
On the occurrence of congruence multiplicities between Ramanujan's theta functions
Shane Chern, Nicolas Allen Smoot, Dazhao Tang
Recently, the first and third authors initiated a study of arithmetical relationships between Ramanujan's theta functions and . In this work, we prove eight families…
math.NT2026
Tadpole Nahm sum as a Wronskian
Shane Chern, Chanh Tran, Tanay Wakhare
We show that the tadpole Nahm sum is essentially a specialization of a series studied by Bartlett and Warnaar. This overlooked connection was first discovered by the internal model…
math.NT2023
Ramanujan's theta functions and internal congruences modulo arbitrary powers of
Shane Chern, Dazhao Tang
In this work, we investigate internal congruences modulo arbitrary powers of for two functions arising from Ramanujan's classical theta functions and . By letting…