This is maybe the first question I actually need to know the answer to! Let $N$ be a positive integer such that $\mathbb{H}/\Gamma(N)$ has genus zero. Then the function field of …

The Gross-Zagier paper "Heegner points and derivatives of $L$-series", is really computational and hard to plow through. It seems it is futile to read it as such and one must look …

I have two different and probably unrelated questions that can both be superficially described by the title, so I hope you'll forgive me if I ask them together. They both fall und …

If you have a lattice $L \subset \mathbb{C}$, you can compute the following numbers: $ G_4(L) = \sum_{\omega \in L, \omega \neq 0} \frac{1}{\omega^4}, \quad G_6(L) = \sum_{\omega …

Does there exist anywhere a comprehensive list of small genus modular curves $X_G$, for G a subgroup of GL(2,Z/(n))$? (say genus <= 2), together with equations? I'm particularly …

Suppose that $f$ is a weight $k$ newform for $\Gamma_1(N)$ with attached $p$-adic Galois representation $\rho_f$. Denote by $\rho_{f,p}$ the restriction of $\rho_f$ to a decomposi …

background/motivation let Ek denote the modular form of level one and weight k with q-expansion given by $E_k(q)=1- \frac{2k}{b_k}\sum_n \sigma_{k-1}(n)q^n$ where σi is th …

People who talk about things like modular forms and zeta functions put a lot of emphasis on the existence and form of functional equations, but I've never seen them used as anythin …

Are there infinitely many (linearly independent) cuspidal eigenforms for $\Gamma(1)$ with integer coefficients? Someone told me that the Hecke algebra is conjectured to act irredu …

First of all, let me apologize in advance for the terseness of this question. It seems that by now there are well-developed techniques (the "Taylor-Wiles-Kisin" method) for provin …

Reading Serre's letter to Gray , I wonder if now modern expositions of the themes in Klein's book exist. Do you know any?

I was hoping that someone could help clarify a source of confusion for me, I must be doing and saying something wrong but I just don't know what: Let $E$ be an elliptic curve over …

I recently realized some kind of analogy when considering modularity results (such as the modularity of elliptic curves over Q). The analogy comes from algebraic groups. Take one p …

Let X_0(p) be the modular curve of level p where p is prime. The Jacobian variety J_0(p) has a natural family of quotients defined over Q with dimensions summing to dim(J_0(p)), ea …

I've been prodded to ask a question expanding this one on Ramanujan's constant exp(π√163). Recall that R = exp(π √163) is very close to an integer; specifically …