# Questions tagged [theta-functions]

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

232 questions
Filter by
Sorted by
Tagged with
197 views

### Summation of $\sum_{n=0}^{\infty}a^nq^{n^2}$

I am trying to find the result for the sum of the form $\sum_{n=0}^{\infty}a^nq^{n^2}$. The special case for $a=1$ is easily given by $\vartheta(0,q)$, where $\vartheta(z,q)$ is the third Jacobi Theta ...
48 views

### What are specific proofs of Jacobi Triple Product Identity?

I am looking for the Special Proofs. Here is a reference from MSE. Motivation for/history of Jacobi's triple product identity I also know that a simple proof via Functional Equation from the book ...
26 views

71 views

39 views

38 views

### Waring problem generalizations and theta-function

My question is twofold: Can the Waring problem be expressed with the Jacobi theta function or some analog (as is the case for $k=2$) for general $k$? Say for $k=4$ or $k=6$, are these able to be ...
110 views

### Theta Functions and Partitions

I am reading some papers by Ramanujan on congruence properties of the partition function. At one point he says that he will be using "theta functions" and introduces the following: It can be shewn ...
78 views

### Formula for sequence $\left(r_{k}\right)_{k=0}^{\infty}=(1, 1, 3, 5, 9, 15, 25, 39, 61, 93,\cdots)$

The sequence $$\left(r_{k}\right)_{k=0}^{\infty}=(1, 1, 3, 5, 9, 15, 25, 39, 61, 93,\cdots)$$ can be found at OEIS as sequence A207641 and is related to Ramanujan theta functions. Unfortunately ...
63 views

### modular forms and their fourier coefficients question

I was recently listening to Don Zagiers fourth lecture at ICTP (posted Feb 5, 2015) on mock modular forms. At roughly 22:00 in the lecture he makes two statements: 1. the product of the weight and ...
36 views

55 views