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SUMMARY:An effective criterion for periodicity of l-adic continued fractio
 ns - Laura Capuano (Oxford)
DTSTART:20190517T150000Z
DTEND:20190517T155000Z
UID:TALK125173@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:It goes back to Lagrange that a real quadratic irrational has 
 always a periodic continued fraction. Starting from decades ago\, several 
 authors proposed different definitions of a l-adic continued fraction\, an
 d the definition depends on the chosen system of residues mod l. It turns 
 out that the theory of l-adic continued fractions has many differences wit
 h respect to the real case\; in particular\, no analogue of Lagrange’s t
 heorem holds\, and the problem of deciding whether the continued fraction 
 is periodic or not seemed to be not known. In recent work with F. Venezian
 o and U. Zannier we investigated the expansion of quadratic irrationals\, 
 for the l-adic continued fractions introduced by Ruban\, giving an effecti
 ve criterion to establish the possible periodicity of the expansion. This 
 criterion\, somewhat surprisingly\, depends on the “real” value of the
  l-adic continued fraction.
LOCATION:MR3 Centre for Mathematical Sciences\, level -1
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