Hostname: page-component-7479d7b7d-t6hkb Total loading time: 0 Render date: 2024-07-14T00:07:43.050Z Has data issue: false hasContentIssue false
  • English
  • Français

On two classical lattice point problems

Published online by Cambridge University Press:  24 October 2008

A. E. Ingham
A. E. Ingham
Affiliation:
King's CollegeCambridge
Get access Rights & Permissions [Opens in a new window]

Extract

1. Let r(n) be the number of representations of n as a sum of two squares, d(n) the number of divisors of n, and

where γ is Euler's constant. Thus P(x) is the error term in the problem of the lattice points of a circle, and Δ(x) the error term in Dirichlet's divisor problem, or the problem of the lattice points of a rectangular hyperbola.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 36 , Issue 2 , April 1940 , pp. 131 - 138
Copyright
Copyright © Cambridge Philosophical Society 1940

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Hardy, G. H. “On Dirichlet's divisor problem.” Proc. London Math. Soc. (2), 15 (1916), 1–25.Google Scholar
(2)Hardy, G. H. and Wright, E. M.An introduction to the theory of numbers (Oxford, 1938).Google Scholar
(3)Ingham, A. E. “A note on the distribution of primes.” Acta arithmetica, 1 (1936), 201–11.CrossRefGoogle Scholar
(4)Landau, E.Vorlesungen über Zahlentheorie (Leipzig, 1927).Google Scholar
(5)Landau, E. “Über diophantische Approximationen.” Scripta Universitatis atque Bibliothecae Hierosolymitanarum (Math. et Phys.), 1 (1923), I.Google Scholar
(6)Thomas, L. H. “An extended form of Kronecker's theorem with an application which shows that Burgers' theorem on adiabatic invariants is statistically true for an assembly.” Proc. Cambridge Phil. Soc. 22 (1925), 886–903.CrossRefGoogle Scholar