On a class of elliptic functions associated with the even Dirichlet characters

Abstract

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 $\wp (z|\tau )$ as the blueprint, we will derive their representations in terms of $q$-series and partial fractions, explore the significance of the coefficients of their power series expansions and establish the modular properties under the actions of the arithmetic groups ${\Gamma }_0(N)$ and ${\Gamma }_1(N)$.