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math.NT2026
An elementary approach to Sun Kim's general theta function identities
Dazhao Tang
Ramanujan's modular equations of degrees , , , and are closely related to certain theta function identities. Warnaar generalized the identities arising from the…
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
Identities and transformations for Lambert series and double Lambert series
Su-Ping Cui, Dazhao Tang
We establish two identities for Lambert series and double Lambert series, thereby resolving conjectures of Andrews, Dixit, Schultz and Yee (Acta Arith.~181:253--286, 2017), as well…