# Tagged Questions

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### Under which constraints are there only finite numbers of irreducible eta product identities?

For the Dedekind eta function, defined as usual by $\eta(q) = q^{\frac1{24}} \prod\limits_{n=1}^{\infty} (1-q^{n})$, let for brevity $e_k:=\eta(q^k)$. An eta product identity (or eta identity for ...
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### Extending the Shimura Lift to Non-Cuspidal Classical Modular Forms of Higher Level

The definition of the Shimura lift of a classical cusp form is well documented. Zagier and Kohnen define a modified version of the lift for a cusp form $g(z)=\sum a(n)q^n \in S_{k+1/2}^{+}(4)$ in the ...
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### The complete list of continued fractions like the Rogers-Ramanujan?

I have two questions about q-continued fractions, but a little intro first. Given Ramanujan's theta function, $$f(a,b) = \sum_{n=-\infty}^{\infty}a^{n(n+1)/2}b^{n(n-1)/2}$$ then the following, ...
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### Linear eta product identities - how many are there?

For the Dedekind eta function, defined as usual by $\eta(q) = q^{\frac1{24}} \prod\limits_{n=1}^{\infty} (1-q^{n})$, let for brevity $e_k:=\eta(q^k)$. With this notation, a blog entry of Michael ...
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### Conformal Mappings for hyperbolic polygon

I am searching for a conformal mapping from the upper halfplane onto a hyperbolic polygon, i.e. the sides of the polygon have to be geodesics. The classical Schwarz Christoffel theorem does the job ...