23
votes
2answers
833 views

A 14th and 26th-power Dedekind eta function identity?

Given the Dedekind eta function $\eta(\tau)$. Let p be a prime and define $m = (p-1)/2$. Let p be a prime of form $p = 12v+5$. Then for $n = 2,4,8,14$: $$\sum_{k=0}^{p-1} \Big(e^{\pi i m k/12} ...
1
vote
0answers
198 views

Dedekind eta function identity involving two complex variables

Given the Dedekind eta function $\eta(\tau)$ and complex numbers a,b with imaginary part > 0, anybody knows how to prove the proposed identity, $$\sum_{k=0}^{p-1} e^{2\pi i ...
3
votes
1answer
448 views

Are there cusp forms for the full modular group Sp(2,Z) and representations det^3 \otimes Sym^2j(\rho_standard)

What are modular forms or cusps forms, resp. ? We start with defining their common domains $\mathbb{H}_g$ as the set of symmetric $g \times g$ matrices with positive definite imaginary parts. The ...
4
votes
0answers
272 views

Weight-2 modular forms under $\Gamma(N)$

I'm looking for explicit bases of weight 2 modular forms under $\Gamma(N)$, for small N (<16 would be enough). (Ideally in terms of Theta- or Eta-Functions) It seems to me that this should ...
7
votes
2answers
1k views

Picard-Fuchs equations for modular functions

Hello, MathOverflow community! Suppose we have a modular curve of genus $0$, whose rational function field is generated by the modular function $f$. We can view $f$ as the parameter for some pencil ...
7
votes
2answers
323 views

What do the numbers G_4 and G_6 of a lattice actually measure?

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 \in L, \omega \neq ...
13
votes
1answer
718 views

What does the incidence algebra of the lattices in C tell us about modular forms?

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 under the category of ...