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Effective irrationality measures via Thue's Fundamentaltheorem and hypergeometric functions

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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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