For questions related to modular forms

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15
votes
2answers
268 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 ...
5
votes
1answer
253 views

Connection between Hecke operators and Hecke algebras

Hecke operators are things that act on modular forms and give rise to a lot of interesting arithmetical results: http://en.wikipedia.org/wiki/Hecke_operator On the other hand on the wikpedia page ...
3
votes
2answers
238 views

Ramanujan congruences and étale cohomology

What is a good reference for the story of congruences such as $$\displaystyle \tau(n) \equiv \sigma(11)(n) \mod\ 691$$ with a conceptual explanation with connections to ├ętale cohomology, etc?
3
votes
2answers
165 views

Reference for Atkin-Lehner theorem

For my understanding of modular forms, I have "properly" read the last chapter of Serre's book on arithmetic. I have not "properly" read the setup of Hecke operators for congruence subgroups. I was ...
7
votes
1answer
330 views

why does a certain formula in Lang's book on modular forms hold?

Background: Let $k$ be an even integer. The Eisenstein series are defined by $$E_{k} = 1 - \frac{2k}{B_{k}}\sum_{n=1}^{\infty} \sigma_{k-1}(n)q^{n}$$ where $$\sigma_{k-1}(n)= \sum\limits_{d \mid ...
2
votes
2answers
823 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 ...
5
votes
1answer
587 views

How are modular forms fundamental operations?

The German mathematician Martin Eichler once stated that there were five fundamental operations of mathematics: addition, subtraction, multiplication, division, and modular forms. This was also ...
7
votes
2answers
510 views

A question on FLT and Taniyama Shimura

Sometime back i watched the documentary of Andrew Wiles proving the Fermat's Last theorem. A truly inspiring video and i still watch it whenever i am in a depressed mood. There are certain ...
7
votes
1answer
361 views

Definition of cusp of a congruence group

I am reading p.22 of Dan Bump's Automorphihic forms and representations. A cusp of the congruence group acting on the upper half plane is defined to be an orbit of the action of the congruence ...