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SUMMARY:Effective irrationality measures via Thue's Fundamentaltheorem and
  hypergeometric functions - Paul Voutier
DTSTART:20100427T133000Z
DTEND:20100427T143000Z
UID:TALK23487@talks.cam.ac.uk
CONTACT:Tom Fisher
DESCRIPTION:Baker obtained the first effective irrationality measures from
  hypergeometric functions in the early 1960's with results like\n\n| (cube
  root of 2) - _p/q_ | > _10^-6^_  _|q|^-2.955^_\,\n\nfor all _p/q_ in _*Q*
 _.\n\nIn fact\, the use of hypergeometric functions for diophantine purpos
 es goes back to Thue. In this lecture\, we investigate such a result of Th
 ue\, Thue's Fundamentaltheorem. We\n* provide a simplified presentation of
  Thue's Fundamentaltheorem\,\n* show how to use it to obtain effective irr
 ationality measures\, \n* prove that it contains Baker's results and their
  refinements as special cases\,\n* show why it holds and new results that 
 follow from this understanding.\n
LOCATION:MR13
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