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SUMMARY:Nicolas Chevallier (Université de Haute Alsace)
DTSTART:20220503T123000Z
DTEND:20220503T133000Z
DTSTAMP:20260423T052838Z
UID:OWNS/84
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/84/">Be
 st Diophantine approximations in the complex plane with Gaussian integers<
 /a>\nby Nicolas Chevallier (Université de Haute Alsace) as part of One Wo
 rld Numeration seminar\n\n\nAbstract\nStarting with the minimal vectors in
  lattices over Gaussian integers in $\\C^2$\, we define a algorithm that f
 inds the sequence of minimal vectors of any unimodular lattice in $\\C^2$.
 \nRestricted to lattices associated with complex numbers this algorithm fi
 nd all the best Diophantine approximations of a complex numbers.\nFollowin
 g Doeblin\, Lenstra\, Bosma\, Jager and Wiedijk\, we study the limit distr
 ibution of the sequence of products $(u_{n1}u_{n2})_n$ where $(u _n=( u_{n
 1}\,u_{n2} ))_n$ is the sequence of minimal vectors of a lattice in $C^2$.
  We show that there exists a measure in $\\C$ which is the limit distribut
 ion of the sequence of products of  almost all unimodular lattices.\n
LOCATION:https://researchseminars.org/talk/OWNS/84/
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