Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-05-22T06:48:25.622Z Has data issue: false hasContentIssue false
  • English
  • Français

Diophantine approximation and Dirichlet series

Published online by Cambridge University Press:  24 October 2008

G. R. Everest
G. R. Everest
Affiliation:
School of Mathematics and Physics, University of East Anglia, Norwich NR4 1TJ
Get access Rights & Permissions [Opens in a new window]

Extract

1. Given a sequence an of positive integers, one expects to obtain information on the distribution of these numbers by examining the Dirichlet series

In this paper we are going to show how such a series arises from Fröhlich's Galoismodule theory and the use the Thue–Siegel–Roth–Schmidt Theorem as one of the tools in the study of its singularities.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 2 , March 1985 , pp. 195 - 210
Copyright
Copyright © Cambridge Philosophical Society 1985

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]Bushnell, C. J.. Diophantine approximation and norm distribution in galois orbits. Illinois J. Math. 27 (1983), 145–157.Google Scholar
[2]Evebest, G. R.. Diophantine approximation and the distribution of normal integral generators. J. London Math. Soc. (2), 28 (1983), 227–237.CrossRefGoogle Scholar
[3]Everest, G. R.. The divisibility of normal integral generators. (To appear.)Google Scholar
[4]Everest, G. R.. Independence problems in the distribution of normal integral generators. (To appear.)Google Scholar
[5]Lang, S.. Algebraic Number Theory (Addison-Wesley, 1970).Google Scholar
[6]Sehgal, S.. Topics in Group Rings (Dekker, 1978).Google Scholar
[7]Taylor, M. J.. On Frohlich's conjecture for rings of integers of tame extensions. Invent. Math. 63 (1981), 41–79.Google Scholar