# Questions tagged [modular-function]

The tag has no usage guidance.

43 questions
Filter by
Sorted by
Tagged with
29 views

### Help me understand the translation between homogeneous elliptic functions and modular functions

I am trying to follow Iwaniec's book on automorphic forms and am getting hung up on the basic definitions. He seems to construct modular forms from elliptic functions and I can't really follow the ...
59 views

### Regarding definitions of modular functions and modular forms

I am self studying Analytic number theory from Apostol Dirichlet series and modular functions in number theory and I have a doubt regarding defintions of modular forms and modular functions. My ...
43 views

102 views

### Generators of the Modular group (Motivation)

I would like to know the motivation of the geometric argument applied on a 'fundamental domain' to get the generators of $SL_2(\mathbb{Z})$. In particular, are there easier examples where this sort of ...
71 views

344 views

### Ramanujan's Class Invariant $G_{625}$

How to calculate the Ramanujan Class Invariant $G_{625}$? Equation is: $x^6-2\varphi^5x^5+2\varphi x+\varphi^6=0$. $\varphi$ is the golden ratio.
81 views

### Examples of modular forms of irrational or complex weights

I think that it is possible to define modular forms of complex weight. But I have never seen modular forms of irrational weight, much less of complex (unreal) weight. If you know any examples of ...
67 views

### Hecke Operator being a modular function

I have a question on http://www.personal.psu.edu/rcv4/567c10.pdf I do not understand the proof of Theorem 10.6. I get that from Theorem 10.5, we get that Tn(f) satisfies the weakly modular equation....
I have read that given a genus 0 modular curve $X$ defined over a base field $k$. The corresponding function field k(X) can be generated by one modular function. I have also read that converse, that ...