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SUMMARY:Transcendence proofs using Mahler functions
DTSTART:20260608T083000Z
DTEND:20260608T093000Z
DTSTAMP:20260712T233600Z
UID:indico-event-16689@indico.math.cnrs.fr
DESCRIPTION:Speakers: Enzo Brechler\n\nProving that a given real number is
  transcendental is in general a difficult problem. In 1929\, Mahler introd
 uced a new method to prove that many numbers such as x=0.1101000100000001.
 .. are transcendental\, giving rise to the class of so-called Mahler funct
 ions. These are analytic functions with algebraic coefficients which satis
 fy a linear difference equation associated to the Mahler operator z->z^q. 
 The theory of Mahler functions has greatly evolved\, to the point that we 
 now have a way to systematically determine if f(alpha) is algebraic or tra
 nscendental when f is a Mahler function and alpha is an algebraic number. 
 One of the main examples of numbers that can be obtained in this way are t
 he automatic numbers such as the Thue-Morse number x=0.110100110010110... 
 In this talk\, I will present the main results on Mahler functions and how
  to apply them concretely to get transcendence results. Furthermore\, I wi
 ll present a generalisation of the theory to the case of Mahler functions 
 of multiple variables\, and show that it gives transcendence results for s
 o-called morphic numbers (an example being the number derived from the Fib
 onacci word x=0.1001010010...\, which is obtained by iterating the substit
 ution rule 0->01\, 1->0).\n\nhttps://indico.math.cnrs.fr/event/16689/
LOCATION:Fokko du Cloux (ICJ)
URL:https://indico.math.cnrs.fr/event/16689/
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