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Bounds for the size of integral solutions to Ym = f(X)

Published online by Cambridge University Press:  20 January 2009

Dimitrios Poulakis
Dimitrios Poulakis
Affiliation:
Aristotle University of Thessaloniki, Department of Mathematics 54006 Thessaloniki, Greece, E-mail address: poulakis@ccf.auth.gr
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Let K be an algebraic number field with ring of integers OK and f(X) ∈ OK[X]. In this paper we establish improved explicit upper bounds for the size of solutions in OK, of diophantine equations Y2 = f(X), where f(X) has at least three roots of odd order, and Ym = f(X), where m is an integer ≥ 3 and f(X) has at least two roots of order prime to m.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 1 , February 1999 , pp. 127 - 141
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

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