Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-13T06:08:43.345Z Has data issue: false hasContentIssue false
  • English
  • Français

Simultaneous asymptotic Diophantine approximations

Published online by Cambridge University Press:  26 February 2010

William W. Adams
William W. Adams
Affiliation:
Institute for Advanced Studies, Princeton. University of California, Berkeley
Get access

Extract

Let θ1, …, θk be k real numbers. Suppose ψ(t) is a positive decreasing function of the positive variable t. Define λ(N), for all positive integers N, to be the number of solutions in integers p1 …, pk, q of the inequalities

and

Type
Research Article
Information
Mathematika , Volume 14 , Issue 2 , December 1967 , pp. 173 - 180
Copyright
Copyright © University College London 1967

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

1.Cassels, J. W. S., An introduction to diophantine approximations (Cambridge, Cambridge University Press, 1957).Google Scholar
2.Cassels, J. W. S., An introduction to the geometry of numbers (Berlin, Springer-Verlag, 1959).CrossRefGoogle Scholar
3.Cassels, J. W. S., “Simultaneous diophantine approximations II”, Proc. Lond. Math. Soc, 5 (1955), 435–448.CrossRefGoogle Scholar
4.Lang, S., “Asymptotic diophantine approximations“, Proc. Nat. Acad. Sci. USA, 55 (1966), 31–34.CrossRefGoogle ScholarPubMed
5.Lang, S., Introduction to diophantine approximations (Reading, Mass., Addison-Wesley, 1966).Google Scholar
6.Popken, J., “Zur Transzendenz von e”, Math. Zeit., 29 (1929), 525–541.CrossRefGoogle Scholar
7.Schmidt, W. M., “A metrical theorem in diophantine approximations”. Canadian J. Math., 11 (1960), 619–631.CrossRefGoogle Scholar
8.Schmidt, W. M., “Simultaneous approximations to a basis of a real algebraic number field”, American J. Math., 88 (1966), 517–527.CrossRefGoogle Scholar