Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-14T22:24:25.886Z Has data issue: false hasContentIssue false

A ‘Hardy–Littlewood’ approach to the norm form equation

Published online by Cambridge University Press:  24 October 2008

G. R. Everest
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ

Extract

Suppose that K is a number field and n = [K: ℚ]. Write S(K) for the set of archimedean places of K, i.e. the set of all embeddings σ: K → ℂ. Suppose that is a linear form in t variables x1, …, xt, where the ajK. This gives rise to a norm form N(x), where

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1988

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]Baker, A. and Masser, D. W.. Transcendence Theory: Advances and Applications (Academic Press, 1977).Google Scholar
[2]Everest, G. R.. Diophantine approximation and the distribution of normal integral generators. J. London Math. Soc. (2) 28 (1983), 227237.CrossRefGoogle Scholar
[3]Everest, G. R.. Angular distribution of units in abelian group rings – an application to Galois-module theory. J. reine angew. Math. 375 (1987), 2441.Google Scholar
[4]Everest, G. R.. Units in abelian group rings and meromorphic functions. Illinois J. Math. (to appear).Google Scholar
[5]Evertse, J.-H.. On sums of S-units and linear recurrences. Compositio Math. 53 (1984), 225244.Google Scholar
[6]Evertse, J.-H. and Györy, K.. On unit equations and decomposable form equations. J. reine angew. Math. 358 (1985), 619.Google Scholar
[7]Schmidt, W. M.. Norm form equations. Ann. of Math. (2) 96 (1972), 526551.CrossRefGoogle Scholar
[8]Schmidt, W. M.. Diophantine Approximation. Lecture notes in Math, vol. 785 (Springer-Verlag, 1980).Google Scholar