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

@article{Chen2020OnAC, title={On a class of elliptic functions associated with even Dirichlet characters}, author={Dandan Chen and Rong Chen}, journal={The Ramanujan Journal}, year={2020}, volume={55}, pages={175-203} }

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 | τ ) 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 $$\Gamma _0(N)$$ Γ 0 ( N ) and…

## One Citation

### A universal identity for theta functions of degree eight and applications

- Mathematics
- 2021

Previously, we proved an identity for theta functions of degree eight, and several applications of it were also discussed. This identity is a natural extension of the addition formula for the…

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