Effective irrationality measures via Thue's Fundamentaltheorem and hypergeometric functions

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• Paul Voutier
• Tuesday 27 April 2010, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Tom Fisher.

Baker obtained the first effective irrationality measures from hypergeometric functions in the early 1960’s with results like

| (cube root of 2) – p/q | > 10^-6 |q|^-2.955,

for all p/q in Q.

In fact, the use of hypergeometric functions for diophantine purposes goes back to Thue. In this lecture, we investigate such a result of Thue, Thue’s Fundamentaltheorem. We

• provide a simplified presentation of Thue’s Fundamentaltheorem,
• show how to use it to obtain effective irrationality measures,
• prove that it contains Baker’s results and their refinements as special cases,
• show why it holds and new results that follow from this understanding.

This talk is part of the Number Theory Seminar series.

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