Tagged Questions

40
votes
3answers
506 views

Proof of $\frac{1}{e^{\pi}+1}+\frac{3}{e^{3\pi}+1}+\frac{5}{e^{5\pi}+1}+\ldots=\frac{1}{24}$

I would like to prove that $\displaystyle\sum_{\substack{n=1\\n\text{ odd}}}^{\infty}\frac{n}{e^{n\pi}+1}=\frac1{24}$. I found a solution by myself 10 hours after I posted it, here it is: ...
0
votes
0answers
30 views

References for the conformal equivalence of the space of complex 1-tori and C?

What are some good references with proofs of the conformal equivalence of the space of complex tori and $\mathbb{C}$? So far I only have the book by Jones and Singerman.
0
votes
0answers
88 views

finding torsion points of elliptic curves on MAGMA

I'm trying to learn how to use MAGMA for computing torsion points (i.e. n-torsion subgroups) of elliptic curves in various field. So far, I've looked in the documentation and other resources and I'm ...
4
votes
0answers
74 views

Connection between modular forms and line bundles

I need a good reference about the connection between modular forms and line bundles. I found only Milne's note that treats briefly this argument. I've already checked, but without finding anything, ...
1
vote
1answer
52 views

Reference for existence of quotients of modular Jacobians?

In the construction of Galois representations attached to modular forms of weight 2, the representation spaces can be found in Tate modules of certain quotients of Jacobians of modular curves by ...
3
votes
1answer
170 views

Preparation for a modular forms course

I'm trying to get a sense of what type of math to brush up on in order to take a course based on the book A First Course in Modular Forms by F. Diamond and J. Shurman. The text claims to be accessible ...
4
votes
1answer
75 views

Reference request: theta functions for lattices which are not unimodular or even

In A Course in Arithmetic, Serre works out some of the theory of theta functions for even, self-dual lattices, e.g. such theta functions are modular forms of weight $n/2$, where $n$ is the dimension ...
13
votes
2answers
242 views

Proving finite dimensionality of modular forms using representation theory?

It is well known how to use algebraic geometry (differentials, divisors, and Riemann-Roch) in order to prove the finite dimensionality of the vector space of modular forms of some fixed weight and ...
2
votes
2answers
688 views

Has Deligne-Rapoport been translated?

The classic text of Deligne and Rapoport giving a model for the mod p reduction of the modular curve is found in a "Lecture Notes in Mathematics" volume. Has it been translated from the original ...