# Tagged Questions

For questions about $\theta$ functions (special functions of several complex variables).

15 views

### Is the $z\gg 1$ behavior of the theta function $\theta_1(z;q)$ known?

Is the $z\gg 1$ behavior of the theta function $\theta_1(z;q)$ known? It seems naively like it could be estimated by a Gaussian integral which would give an answer along the lines of $e^{bz^2}$ for ...
40 views

63 views

### Derivation of Transformation for basic theta function

Given that $\vartheta(x) = \sum_{n = -\infty}^\infty e^{-\pi n^2 x}$, I am trying to finish a derivation that $\vartheta(x) = \frac{1}{\sqrt{x}}\vartheta(1/x)$. I believe that I am very close. I ...
43 views

64 views

299 views

282 views

### Theta function: Absolute convergence

I have to proof that the series $$\theta (z)= \sum_{n=-\infty}^{+\infty} e^{\pi i [n^{2} \tau + 2nz]}$$ converges absolutely and uniformly on compact subsets of $\mathbb{C}$. Necessary and sufficient ...
513 views

492 views

197 views

### What is meant by a set of generic points on a compact Riemann surface

Let $X$ be a compact connected Riemann surface of genus $g \geq 1$. I'm studying a theorem of Faltings which looks as follows. Let $P_1,\ldots, P_g$ be generic points on $X$. Then we have some ...
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 ...