On a class of elliptic functions associated with even Dirichlet characters

Abstract

We construct a class of companion elliptic functions associated with even Dirichlet characters. Using the well-known properties of the classical Weierstrass elliptic function $$\wp (z|\tau )$$ as a blueprint, we will derive their representations in terms of q-series and partial fractions. We also 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 $$\Gamma _1(N)$$ .