Work

Numerical experiments on the Hardy conjecture for the Gauss circle problem

Year: 2026

Type: preprint

Abstract: The classical unsolved Gauss circle problem concerns estimating the error between the number of lattice points inside a circle and the area of the circle as its radius tends to infinity. About a century ago, Hardy proposed a conjecture concerning this problem. In this paper, we attempt to provide numerical evidence in support of the Hardy conjecture through large-scale numerical computations.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.04725

Authors: Yamaguchi, Satoshi, Fujima, Shoichi, Kuratsubo, Shigehiko, Nakai, Eiichi, Yoneda, Tsuyoshi

Institutions: Hitotsubashi University, Ibaraki University, Hirosaki University

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: University of Tokyo, Japan Society for the Promotion of Science, RIKEN

Awards: 平均値・平均振動量・増大度が一様でない Banach 関数空間の理論と応用, 平均振動量・増大度が一様でない関数空間の理論と応用, G7803507214, Creation of machine learning theory for solving turbulent closure problems through collaboration between physics and mathematics

OpenAlex ID: W7211891784

Cites: 3

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Related to: 10