On the remainder term in the circle problem in an arithmetic progression

TL;DR

This paper improves the estimate of the error term in the asymptotic formula for the circle problem within arithmetic progressions, advancing understanding of lattice point distribution.

Contribution

It provides a sharper bound for the remainder term in the circle problem specifically in arithmetic progressions, enhancing previous estimates.

Findings

Improved the upper bound for the remainder term.

Refined techniques for analyzing lattice points in arithmetic progressions.

Enhanced understanding of the distribution of lattice points in geometric regions.

Abstract

In this paper we improve the estimate for the remainder term in the asymptotic formula concerning the circle problem in an arithmetic progression.