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SUMMARY:James Worrell (University of Oxford)
DTSTART:20230919T120000Z
DTEND:20230919T130000Z
DTSTAMP:20260423T053048Z
UID:OWNS/117
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/117/">T
 ranscendence of Sturmian Numbers over an Algebraic Base</a>\nby James Worr
 ell (University of Oxford) as part of One World Numeration seminar\n\n\nAb
 stract\nFerenczi and Mauduit showed in 1997 that a number represented over
  an integer base by a Sturmian sequence of digits is transcendental.  In t
 his talk we generalise this result to hold for all algebraic number base b
  of absolute value strictly greater than one.  More generally\, for a give
 n base b and given irrational number θ\, we prove rational linear indepen
 dence of the set comprising 1 together with all numbers of the above form 
 whose associated digit sequences have slope θ.\n\nWe give an application 
 of our main result to the theory of dynamical systems. We show that for a 
 Cantor set C arising as the set of limit points of a contracted rotation f
  on the unit interval\, where f is assumed to have an algebraic slope\, al
 l elements of C except its endpoints 0 and 1 are transcendental.\n\nThis i
 s joint work with Florian Luca and Joel Ouaknine.\n
LOCATION:https://researchseminars.org/talk/OWNS/117/
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