The definitive solution of Gauss’s lattice points problem in the circle

Aldo Peretti
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 22, 2016, Number 2, Pages 1–3
Full paper (PDF, 464 Kb)

Details

Authors and affiliations

Aldo Peretti
Murillo 1131, 9) “D” (1414) Buenos Aires, Argentina

Abstract

By means of Bienayme’s theorem of Statistics is found that the remainder term in Gauss’s problem about the lattice points in the circle is a function normally distributed with mean value zero and standard deviation 1,10368 multiplied by the fourth root of x. This result can not be improved.

Keywords

• Lattice points in the circle
• Bienayme’s theorem

AMS Classification

• Primary: 11P29, 11H06, 11H31, 52C05
• Secondary: 11D45

References

1. Landau, E. (1947) Vorlesungen Uber Zahlentheorie, Chelsea Publishing Company, NewYork.