The distribution of lattice points with relatively r-prime

Wataru Takeda

The distribution of lattice points with relatively r-prime

Number Theory 2017-04-10 v1

Authors: Wataru Takeda

Abstract

The distribution of lattice points with relatively $r$ -prime is related to problems in the Number Theory such as the Extended Lindel\"{o}f Hypothesis and the Gauss Circle Problem. It is known that Sittinger's result is improved on the assumption of the Extended Lindel\"{o}f Hypothesis. In this paper, we improve Sittinger's result without assuming the Extended Lindel\"{o}f hypothesis.

Keywords

lattice points relatively r-prime number theory Extended Lindelöf Hypothesis Gauss Circle Problem Sittinger's result distribution

Cite

@article{arxiv.1704.02115,
  title  = {The distribution of lattice points with relatively r-prime},
  author = {Wataru Takeda},
  journal= {arXiv preprint arXiv:1704.02115},
  year   = {2017}
}

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6 pages

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