Gauss Sphere Problem with Polynomials

This paper provides an estimate of the sum of a homogeneous polynomial $P$ of degree $ν$ and mean zero over the lattice points inside a sphere of radius $R$. It is proved that $\sum_{\mathbf x \in \mathbb Z^3 \atop |\mathbf x| \le R} P(\mathbf x) = O_{ε,P}(R^{ν+ 83/64 + ε})$

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