So Euler employed the following identity $$\sin(z) = z \prod_{n=1}^{\infty} \left[1-\left(\frac{z}{n\pi}\right)^{2}\right]$$
to evaluate $\zeta(2n)$, for $n\in\mathbb{N}$
I'm curious if there's been any research on an elliptic generalization of Euler's trick, replacing $\sin(z)$ with the Jacobi elliptic function $\mathrm{sn}(z,k)$ -- my attempts at googling "elliptic zeta function" are somewhat frustrated by the existence of the Weierstrass zeta function, and zeta functions of an elliptic curve, and it is unclear to me whether the elliptic zeta functions mentioned in this article correspond to the same iceberg that I am suggesting above.