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Congruence modulo 4 for Andrews' integer partition with even parts below odd parts
Dandan Chen, Rong Chen
We find and prove a class of congruences modulo 4 for Andrews' partition with certain ternary quadratic form. We also discuss distribution of and furth…
Congruences modulo powers of 5 for the rank parity function
Dandan Chen, Rong Chen, Frank Garvan
It is well known that Ramanujan conjectured congruences modulo powers of 5, 7 and and 11 for the partition function. These were subsequently proved by Watson (1938) and Atkin (1967…
On Decomposition of as the Sum of Lambert Series and Cusp forms
Dandan Chen, Rong Chen
Based on the values of the Weierstrass elliptic function at , and the theory of modular forms on the arithmetic group $Γ_0(2…
On a class of elliptic functions associated with the even Dirichlet characters
Dandan Chen, Rong Chen
We construct a class of companion elliptic functions associated with the even Dirichlet characters. Using the well-known properties of the classical Weierstrass elliptic function $…
Representations of mock theta functions
Dandan Chen, Liuquan Wang
Motivated by the works of Liu, we provide a unified approach to find Appell-Lerch series and Hecke-type series representations for mock theta functions. We establish a number of pa…