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https://feeds.library.caltech.edu/people/Keller-H-B/monograph.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 13:47:11 +0000Numerical Studies of the Gauss Lattice Problem
https://resolver.caltech.edu/CaltechAUTHORS:20091022-102132378
Authors: {'items': [{'id': 'Keller-H-B', 'name': {'family': 'Keller', 'given': 'H. B.'}}]}
Year: 1997
The difference between the number of lattice points N(R) that lie in x^2 + y^2 ≤ R^2 and the area of that circle, d(R) = N(R) - πR^2, can be bounded by |d(R)| ≤ KR^θ.
Gauss showed that this holds for θ = 1, but the least value for which it holds is an open problem in number
theory. We have sought numerical evidence by tabulating N(R) up to R ≈ 55,000. From the convex hull bounding log |d(R)| versus log R we obtain the bound θ ≤ 0.575, which is significantly better than the best analytical result θ ≤ 0.6301 ... due to Huxley. The behavior of d(R) is of interest to those studying quantum chaos.https://authors.library.caltech.edu/records/prnc0-n1f53