On the Solution of Gauss Circle Problem Conjecture (Revised)

TL;DR

This paper provides an asymptotic formula for the average number of representations of integers as sums of two squares, advancing understanding of the Gauss circle problem.

Contribution

It offers a revised asymptotic formula for the mean value in the Gauss circle problem, improving previous estimates.

Findings

Derived a new asymptotic expression for the mean value

Enhanced understanding of the distribution of sums of two squares

Provides a refined approach to the Gauss circle problem

Abstract

We give an asymptotic formula for the mean value of the number of representations of an integer as sum of two squares known as the Gauss circle problem.