On the average sum of the $k$-th divisor function over values of quadratic polynomials

Kostadinka Lapkova, Nian Hong Zhou

Let $F(\mathbf{x})\in \mathbb{Z}[x_1,x_2,\dots ,x_n]$ be a quadratic polynomial in $n\ge 3$ variables with a nonsingular quadratic part. Using the circle method we derive an asymptotic…