Abstract We find and prove a class of congruences modulo 4 for eta-products associated with certain ternary quadratic forms. This study was inspired by similar conjectured congruences modulo 4 for… Expand

International audience
It is well known that Ramanujan conjectured congruences modulo powers of 5, 7 and 11 for the partition function. These were subsequently proved by Watson (1938) and Atkin… Expand

We find and prove a class of congruences modulo 4 for Andrews’ partition with certain ternary quadratic form. We also discuss distribution of EO(n) and further prove that EO(n) ≡ 0 (mod 4) for almost… Expand

We construct a class of companion elliptic functions associated with even Dirichlet characters. Using the well-known properties of the classical Weierstrass elliptic function $$\wp (z|\tau )$$ ℘ ( z… Expand

We find Hecke-Rogers type series representations of generating functions of the Hurwitz class numbers which are similar to certain mock theta functions. We also prove two combinatorial… Expand

Based on the values of the Weierstrass elliptic function $$\wp (z|\tau )$$
at $$z=\pi \tau /2$$
, $$(\pi +\pi \tau )/{2}, (\pi +\pi \tau )/{4},(\pi +2\pi \tau )/{4}$$
and the theory of modular… Expand

Based on the values of the Weierstrass elliptic function $\wp(z|\tau)$ at $z=\pi\tau/2$, $(\pi+\pi\tau)/{2}, (\pi+\pi\tau)/{4},(\pi+2\pi\tau)/{4}$ and the theory of modular forms on the arithmetic… Expand