# Questions tagged [dedekind-eta-function]

Use this tag for questions about a particular function defined on the upper half-plane of complex numbers and that is a modular form of weight one-half.

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### how to evaluate the explicit formula for the quotient powers of the Dedekind eta function

I'm working on a thesis in number theory, specifically focusing on modular forms, particularly the Dedekind eta functions. I want to know if there is a way to obtain the explicit expression for the ...
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### The Dedekind eta function $\eta(\tau)=q^{\frac{1}{24}} \prod_{n=1}^\infty (1-q^n)$ and $|\tau|^{1/2} |\eta(\tau)|^2$

I tried to prove the standard identities of the Dedekind eta function $$\eta(\tau)=q^{\frac{1}{24}} \prod_{n=1}^\infty (1-q^n),$$ where $q=\exp(2\pi i \tau)$ for some complex number $\tau$, but ...
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### Location of the zeros of Dedekind Eta Function

Just a fast question, since I have not been able to find any answer for it online. Where are the zeros of Dedekind eta function $\eta(s)$ located? Apart from the trivial one as $s \to i \infty$, ...
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### How to derive relationship between Dedekind's $\eta$ function and $\Gamma(\frac{1}{4})$

I am trying to determine in what way to approach finding a connection between Dedekind's Eta Function, defined as $$\eta(\tau)=q^\frac{1}{24}\prod_{n=1}^\infty(1-q^n)$$ where $q=e^{2\pi i \tau}$ is ...
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### Modular transformations of $\eta(\tau)$
Under a modular transformation the Dedekind $\eta$ function transforms as $$\eta(-1/\tau) = \sqrt{-i \tau}\eta(\tau) \, .\tag*{(*)}$$Siegel gives a proof in this paper here that uses complex ...
### Which role does the $\frac{1}{24}$ in the Dedekind $\eta$-function play?
The Dedekind $\eta$-function is defined as $$\eta(z) = q^{\frac{1}{24}} \prod_{n = 1}^\infty (1 - q^n)^{-1}$$ where $q = e^{2 \pi i z}$. My question is: If I start with the Euler-product \$\prod_{n = ...