English

Gauss Sphere Problem with Polynomials

Number Theory 2013-12-03 v1

Abstract

This paper provides an estimate of the sum of a homogeneous polynomial PP of degree ν\nu and mean zero over the lattice points inside a sphere of radius RR. It is proved that xZ3xRP(x)=Oϵ,P(Rν+83/64+ϵ) \sum_{\mathbf x \in \mathbb Z^3 \atop |\mathbf x| \le R} P(\mathbf x) = O_{\epsilon,P}(R^{\nu + 83/64 + \epsilon})

Keywords

Cite

@article{arxiv.1312.0108,
  title  = {Gauss Sphere Problem with Polynomials},
  author = {Fan Zheng},
  journal= {arXiv preprint arXiv:1312.0108},
  year   = {2013}
}

Comments

34 pages, 1 table

R2 v1 2026-06-22T02:18:05.908Z