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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.

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    Don't know if it's useful, but the only product formula for sn listed at the Wolfram functions site is this: http://functions.wolfram.com/EllipticFunctions/JacobiSN/08/.2011-06-14
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    That factorization for sine is a special case of the [Weierstrass factorization theorem](http://en.wikipedia.org/wiki/Weierstrass_factorization_theorem) (which [applies to the Riemann $\zeta$ function](http://en.wikipedia.org/wiki/Riemann_zeta_function#Hadamard_product) similarly). A Jacobi elliptic function has poles so it isn't entire, but it is meromorphic so it can be written as the quotient of two holomorphic functions, and each of these can then be factored. Personally I'm more interested in the infinite product representation itself than analogizing Euler's zeta trick.2011-07-30
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    "as the quotient of two holomorphic functions" - more specifically, remember that the Jacobian elliptic functions are in fact ratios of theta functions.2011-07-30

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