# Questions tagged [theta-functions]

For questions about $\theta$ functions (special functions of several complex variables).

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### Intuition behind theta function L-series correspondence

I know that we can analytically continue $L$-series by taking the Mellin transform of a sutiable theta function. Technically we need a transformation law for the theta function at $0$ and $\infty$ as ...
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### A series in terms of the Jacobi theta fuctions

On Wikipedia, one can find an expression of the series $$\sum_{n=1}^\infty \frac{n^pq^n}{1-q^n}$$ in terms of the Jacobi theta functions for $p=3,5,7$. I'm looking for an expression of this series ...
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### Summation in the form of Jacobi Theta Function

TL;DR: My summation should give the same result when it is expressed as the Jacobi Theta function. It gives the same results for some set of inputs but then gives exactly the half of it for other set ...
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### Is there any definition for this series function $f(s)=\sum_{n=1}^\infty e^{-n^s}$?

What I am asking for is if there is any theory related to this real series $f(s)=\sum_{n=1}^\infty e^{-n^s}$ and $s\ge 1$. As far as I know, if $s = 1$, it's a simple geometric series, and if $s = 2$, ...
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1 vote
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### Can I express this sum as product of two theta functions?

I have an infinite sum written as $$\sum_{mn} e^{-i2\pi(m c_1 +n c_2)} e^{-(m^2+n^2-mn)}$$ where $m,n$ are integers, $0<c_1, c_2<1$. I want to express the above expression into a product of ...
1 vote
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