# Tagged Questions

A modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group.

95 views

### What do mathematicians mean when they say “form”?

As in differential form, modular form, quadratic form? I'm sorry if this is a really silly question.
24 views

### Modular forms under isogenies

Let $f$ be a modular form of level 1, say an Eisenstein series to simplify. If $n$ is a natural number, what can we say about $f(n\tau)$ in terms of $f(\tau)$?
149 views
+100

### Why are $L$-functions a big deal?

I've been studying modular forms this semester and we did a lot of calculation of $L$-functions, e.g. $L$-functions of Dirichlet-characters and $L$-functions of cusp-forms. But I somehow don't see, ...
31 views
+50

### References on Hauptmoduln

Here it is said that a Hauptmodul (a generator of a modular function field) is unique up to a Möbius transformation. My impression is that it is really hard to find references on Hauptmoduln and ...
26 views

### Calculation of a limit including the Dedekind eta function

I do not understand this attached equation, where $\eta$ means the Dedekind eta function and $E_2$ the Eisenstein series of weight $2$. Has someone an idea what happens here?
28 views

84 views

### Modular transformations of $\eta(\tau)$

Under a modular transformation the Dedekind $\eta$ function transforms as $$\eta(-1/\tau) = \sqrt{-i}\eta(\tau).\tag*{(*)}$$Siegel gives a proof in this paper here that uses complex analytic ...
155 views

### Why is 12 the smallest weight for which a cusp forms exists

On wikipedia (here) I have read the following: Twelve is the smallest weight for which a cusp form exists. [...] This fact is related to a constellation of interesting appearances of the number ...
37 views

42 views

### Proving $\zeta(3)\in\mathbb{R}\setminus\mathbb{Q}$ using modular forms

I am looking for references proving $\zeta(3)\in\mathbb{R}\setminus\mathbb{Q}$ using modular forms, like this paper written by F. Beukers. Does anybody know some different papers or books? Thanks.
23 views

52 views

### $p$-depletion of a modular form

Let $p$ a prime and $N$ an integer such that $p\not\mid N$. I will denote with $X_0(m)$ the modular curve with respect to the congruence subgroup $\Gamma_0(m)$. Let $f$ be a modular form with ...