The sum of multidimensional divisor function over values of quadratic polynomial

Let $F({\bf x})={\bf x}^tQ_m{\bf x}+$\mathbf{b}$^t{\bf x}+c\in$\mathbb{Z}$[{\bf x}]$beaquadraticpolynomialin$\ell (\ge 3 )$variables${\bf x} =(x_{1},…,x_{\ell})$,where$F({\bf x})$ispositivewhen${\bf x}\in$\mathbb{R}${\ge 1}^{\ell}$,$Q_m\in {\rm M}{\ell}($\mathbb{Z}$)$isan$\ell\times\ell$matrixanditsdiscriminant$\det\left(Q_m^t+Q_m\right)\neq 0$. It gives explicit asymptotic formulas for the following sum $$T_{k,F}(X)=\sum _{\mathbf{x}\in [1,X{]}^{\mathrm{\ell }}\cap {\mathbb{Z}}^{\mathrm{\ell }}}{\tau }_k(F(\mathbf{x}))$$ with the help of the circle method. Here ${\tau }_k(n)=\mathrm{\#}\{(x_1,x_2,\mathrm{.}\mathrm{.}\mathrm{.},x_k)\in {\mathbb{N}}^k:n=x_1{x}_2\mathrm{.}\mathrm{.}\mathrm{.}{x}_k\}$ with $k\in {\mathbb{Z}}_{\ge 2}$ is the multidimensional divisor function.