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高斯圆问题的哈代猜想的数值实验

Numerical experiments on the Hardy conjecture for the Gauss circle problem

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

arXiv 2609.04725首次发表:更新:

AI 中文总结

本文针对经典高斯圆问题,通过大规模数值计算,为约一个世纪前哈代提出的相关猜想提供数值证据支持。

AI 中文摘要

经典的未解决高斯圆问题涉及估计当半径趋于无穷时,圆内格点数量与圆面积之间的误差。约一个世纪前,哈代针对该问题提出了一个猜想。本文试图通过大规模数值计算,为哈代猜想提供数值证据支持。

英文摘要

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.

Comments14 pages, 15 figures, 6 FORTRAN programs

论文原文

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