(notation from http://mathworld.wolfram.com/JacobiThetaFunctions.html … assuming z=0) Θ₁=0. M(Θ₄)=ζ-2ζ₂,where ζ₂ is the ζ function of the Dirichlet character modulo 2, and ζ is the original ζ function. M(Θ₃)=ζ.
Do we know what L-functions we get from Mellin transforms of the other 3 Jacobian theta functions? (all four of these are likely not algebraically independent)
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I'm not sure whether M(Θ₂) is really a L-function, as M(Θ₂)(s) is something involving ζ(s-1/2).
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Maybe Mathoverflow the problem?
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