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Let $Q$ be a four-variable positive-definite quadratic form with integer coefficients and let $r_{Q}(n)$ be the number of representations of $n$ by $Q$. The theory of modular forms explains how $r_{Q}(...

I have asked this question exactly here. The question is as follows: I am interested deeply in the following problem: Let $f$ be a (fixed) positive definite quadratic form; and let $n$ be an ...

Siegel's formula(Siegel-Weil) directly relates the weighted sum of theta functions to Eisenstein series. (Or equivalently, the weighted sum of the cusp form is zero). I wonder if there is a ...

Define the function $$f(q,z,y) = \sum_{n \ge 0,m,l} c(n,m,l) q^n z^m y^l$$ where $c(n,m,l)$ is defined by $$ c(n,m,l) = \begin{cases} (-1)^{s+l} & \text{if } 4n - m^2 + l^2 = 2s(s+1)\\ 0 & \...