Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-18T16:38:13.285Z Has data issue: false hasContentIssue false
  • English
  • Français

The inhomogeneous minimum of binary quadratic forms

Published online by Cambridge University Press:  24 October 2008

Daniel Berend  and
William Moran
Daniel Berend
Affiliation:
Department of Mathematics, University of Texas, Austin, TX 78712, U.S.A.
William Moran
Affiliation:
Department of Pure Mathematics, University of Adelaide, Adelaide, S.A. 5001, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

An indefinite binary quadratic form ƒ gives rise to a certain function M on the torus. The properties of M, especially those related to its maximum – the so-called inhomogeneous minimum of ƒ – are the subject of numerous papers. Here we continue this study, putting more emphasis on the general behaviour of M.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 1 , July 1992 , pp. 7 - 19
Copyright
Copyright © Cambridge Philosophical Society 1992

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]Adler, R. L. and Weiss, B.. Similarity of Automorphisms of the Torus. Memoirs Amer. Math. Soc. no. 98 (American Mathematical Society, 1970).CrossRefGoogle Scholar
[2]Barnes, E. S.. The inhomogeneous minima of binary quadratic forms. IV. Acta Math. 92 (1954), 235–264.CrossRefGoogle Scholar
[3]Barnes, E. S. and Swinnerton-Dyer, H. P. F.. The inhomogeneous minima of binary quadratic forms. I. Acta Math. 87 (1952), 259–323.CrossRefGoogle Scholar
[4]Barnes, E. S. and Swinnerton-Dyer, H. P. F.. The inhomogeneous minima of binary quadratic forms. II. Acta Math. 88 (1952), 279–316.CrossRefGoogle Scholar
[5]Barnes, E. S. and Swinnerton-Dyer, H. P. F.. The inhomogeneous minima of binary quadratic forms. III. Acta Math. 92 (1954), 199–234.CrossRefGoogle Scholar
[6]Berend, D.. Minimal sets on tori. Ergodic Theory Dynamical Systems 4 (1984), 499–507.CrossRefGoogle Scholar
[7]Cassels, J. W. S.. An Introduction to Diophantine Approximation (Cambridge University Press, 1965).Google Scholar
[8]Denker, M., Grillenberger, C. and Sigmund, K.. Ergodic Theory on Compact Spaces (Springer-Verlag, 1976).CrossRefGoogle Scholar
[9]Furstenberg, H.. Disjointness in ergodic theory, minimal sets and a problem in diophantine approximations. Math. Systems Theory 1 (1967), 1–49.CrossRefGoogle Scholar
[10]Furstenberg, H.. Recurrence in Ergodic Theory and Combinatorial Number Theory (Princeton University Press, 1981).CrossRefGoogle Scholar
[11]Lekkerkerker, C. G.. Geometry of Numbers (Wolters-Noordhoff and North-Holland, 1969).Google Scholar
[12]Peres, Y.. Personal communication.Google Scholar
[13]Walters, P.. An Introduction to Ergodic Theory (Springer-Verlag, 1981).Google Scholar