The explicit asymptotic formula of divisor function on average over values of quadratic polynomial

Nianhong Zhou

Let $F(\mathbf{x})={\mathbf{x}}^t{Q}_{\mathbf{x}}+{\mathbf{b}}^t\mathbf{x}+c\in \mathbb{Z}[\mathbf{x}]$ be a quadratic polynomial in $\ell (\ge 3)$ variables $\mathbf{x}=(x_1,...,x_{\ell })$, where $F({\b…