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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

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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