University of Cambridge > Talks.cam > Number Theory Seminar > Effective irrationality measures via Thue's Fundamentaltheorem and hypergeometric functions

Effective irrationality measures via Thue's Fundamentaltheorem and hypergeometric functions

Add to your list(s) Download to your calendar using vCal

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.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2019 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity