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The S-unit equation over function fields

Published online by Cambridge University Press:  24 October 2008

Joseph H. Silverman
Joseph H. Silverman
Affiliation:
Mathematics Department, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, U.S.A.
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In the study of integral solutions to Diophantine equations, many problems can be reduced to that of solving the equation

in S-units of the given ring. To accomplish this over number fields, the only known effective method is to use Baker's deep results on linear forms in logarithms, which yield relatively weak upper bounds. For function fields, R. C. Mason [2] has recently given a remarkably strong effective upper bound. In this note we give an independent proof of Mason's bound, relying only on elementary algebraic geometry, principally the Riemann-Hurwitz formula.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 1 , January 1984 , pp. 3 - 4
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

[1] Hartshorne, R.Algebraic Geometry (Springer-Verlag, 1977).Google Scholar
[2] Mason, R. C.. The hyperelliptic equation over function fields. Math. Proc. Cambridge Philos. Soc. 93 (1983), 219–230.Google Scholar