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SUMMARY:Pieter Allaart (University of North Texas)
DTSTART:20211102T133000Z
DTEND:20211102T143000Z
DTSTAMP:20260423T021449Z
UID:OWNS/63
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/63/">On
  the existence of Trott numbers relative to multiple bases</a>\nby Pieter 
 Allaart (University of North Texas) as part of One World Numeration semina
 r\n\n\nAbstract\nTrott numbers are real numbers in the interval $(0\,1)$ w
 hose continued fraction expansion equals their base-$b$ expansion\, in a c
 ertain liberal but natural sense. They exist in some bases\, but not in al
 l. In a previous OWNS talk\, T. Jones sketched a proof of the existence of
  Trott numbers in base 10. In this talk I will discuss some further proper
 ties of these Trott numbers\, and focus on the question: Can a number ever
  be Trott in more than one base at once? While the answer is almost certai
 nly "no"\, a full proof of this seems currently out of reach. But we obtai
 n some interesting partial answers by using a deep theorem from Diophantin
 e approximation.\n
LOCATION:https://researchseminars.org/talk/OWNS/63/
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