We apply the circle method with a Gaussian weight to obtain an asymptotic formula for the density of representations of non-zero integers by non-singular quadratic forms in at least four variables.
On a form of degree $d$ in $2d+1$ variables ($d\geq 4$)
An Elementary Proof of an Asymptotic Formula of Ramanujan
Asymptotics for numbers of line segments and lines in a square grid
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