The distribution of lattice points with relatively r-prime
Wataru Takeda
TL;DR
This paper improves previous results on the distribution of lattice points with relatively r-prime, removing the need for the Extended Lindelöf Hypothesis, thus advancing understanding in number theory problems like the Gauss Circle Problem.
Contribution
It provides an improved bound on the distribution of lattice points with relatively r-prime without relying on the Extended Lindelöf Hypothesis.
Findings
Enhanced bounds on lattice point distribution
No assumption of Extended Lindelöf Hypothesis needed
Progress in number theory related to the Gauss Circle Problem
Abstract
The distribution of lattice points with relatively -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.
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Taxonomy
TopicsAnalytic Number Theory Research · Limits and Structures in Graph Theory · Algebraic Geometry and Number Theory