Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-30T19:54:02.062Z Has data issue: false hasContentIssue false
  • English
  • Français

Two classical lattice point problems

Published online by Cambridge University Press:  24 October 2008

K. S. Gangadharan  and
A. E. Ingham
K. S. Gangadharan
Affiliation:
Department of MathematicsUniversity of Ceylon
Get access Rights & Permissions [Opens in a new window]

Extract

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. Then P(x) is the error term in the problem of the lattice points of the circle, and Δ(x) the error term in Dirichlet's divisor problem, or the problem of the lattice points of the rectangular hyperbola.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 4 , October 1961 , pp. 699 - 721
Copyright
Copyright © Cambridge Philosophical Society 1961

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)Besicovitch, A. S., On the linear independence of fractional powers of integers. J. London Math. Soc. 15 (1940), 3–6.Google Scholar
(2)Bohr, H. and Jessen, B., One more proof of Kronecker's theorem. J. London Math. Soc. 7 (1932), 274–5.CrossRefGoogle Scholar
(3)Cassels, J. W. S., An introduction to Diophantine approximation (Cambridge, 1957).Google Scholar
(4)Hardy, G. H.On Dirichlet's divisor problem. Proc. London Math. Soc. (2), 15 (1916), 1–25.Google Scholar
(5)Hardy, G. H., On the expression of a number as the sum of two squares. Quart. J. Math. 46 (1915), 263–83.Google Scholar
(6)Ingham, A. E., On two classical lattice point problems. Proc. Cambridge Philos. Soc. 36 (1940), 131–8.CrossRefGoogle Scholar
(7)Landau, E., Vorlesungen über Zahlentheorie, Bd. 2 (Leipzig, 1927).Google Scholar