English

Estimates on Lattice Points in the Circle

Number Theory 2014-09-09 v1

Abstract

This paper provides estimates on the difference between the number of integer lattice points an a circle centered at the origin and the area. The estimates have the form "Big O" of the product of logarithm of the radius and the radius raised to a power 2b. The simplest new estimate obtained is b = 5/16; the best is b = 1507/4875 = .309128205...

Cite

@article{arxiv.1409.2446,
  title  = {Estimates on Lattice Points in the Circle},
  author = {Julius L. Shaneson},
  journal= {arXiv preprint arXiv:1409.2446},
  year   = {2014}
}
R2 v1 2026-06-22T05:51:37.253Z