On a class of elliptic functions associated with even Dirichlet characters
Tóm tắt
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
$$\Gamma _1(N)$$
.
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