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SUMMARY:On the p-adic Littlewood conjecture for quadratics - Bengoechea\, 
 P (University of York)
DTSTART:20140627T133000Z
DTEND:20140627T143000Z
UID:TALK53201@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Let |||| denote the distance to the nearest integer and\, for 
 a prime number p\, let ||_p denote the p-adic absolute value. In 2004\, de
  Mathan and Teuli asked whether $inf_{q?1} q||qx|||q|_p = 0$ holds for eve
 ry badly approximable real number x and every prime number p. When x is qu
 adratic\, the equality holds and moreover\, de Mathan and Teulli proved th
 at $lim inf_{q?1} qlog(q)||qx|||q|_p$ is finite and asked whether this lim
 it is positive.\nWe give a new proof of de Mathan and Teulli's result by e
 xploring the continued fraction expansion of the multiplication of x by p 
 with the help of a recent work of Aka and Shapira. We will also discuss th
 e positivity of the limit.  \n\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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