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Norm form equations. III: positive characteristic

Published online by Cambridge University Press:  24 October 2008

R. C. Mason
R. C. Mason
Affiliation:
Gonville and Caius College, Cambridge
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Extract

This paper aims to provide a complete resolution of the general norm form equation over function fields of positive characteristic. In a previous paper [4] we studied norm forms in the simpler case of zero characteristic; that study forms the starting point for the present investigations. Diophantine problems over function fields of positive characteristic were first investigated by Armitage in 1968 [1], who clamied to have established an analogue of the Thue–Siegel–Roth–Uchiyama theorem for such fields. This claim was refuted by Osgood in 1975 [6], who also derived a correct analogue of Thue's approximation theorem. in 1983 a different attack was made on Diophantine problems over function fields, the principal weapon being a bound [2] for the heights of the solutions of the unit equation

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 3 , May 1986 , pp. 409 - 423
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1]Armitage, J. V.. The Thue-Siegel-Roth theorem in characteristic p. J. Algebra 9 (1968), 183–189.CrossRefGoogle Scholar
[2]Mason, R. C.. The hyperelliptic equation over function fields. Math. Proc. Cambridge Philos. Soc. 93 (1983), 219–230.CrossRefGoogle Scholar
[3]Mason, R. C.. Diophantine Equations over Function Fields. London Math. Soc. Lecture Notes 96 (Cambridge University Press, 1984).CrossRefGoogle Scholar
[4]Mason, R. C.. Norm form equations I. J. Number Theory (in the Press).Google Scholar
[5]Mason, R. C.. Norm form equations II: decomposable forms (in the Press).Google Scholar
[6]Osgood, C. F.. Effective bounds on the ‘Diophantine approximation’ of algebraic functions over fields of arbitrary characteristic and applications to differential equations. Indag. Math. 37 (1975), no. 2, 105–119.CrossRefGoogle Scholar
[7]Schmidt, W. M.. Norm form equations. Ann. Math. 96 (1972), 526–661.Google Scholar
[8]Brownawell, W. D. and Masser, D. W.. Vanishing sums in function fields. Math. Proc. Cambridge Philos. Soc. 100 (1986) (in the Press).Google Scholar