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SUMMARY:Francesco Veneziano (University of Genova)
DTSTART:20201006T123000Z
DTEND:20201006T133000Z
DTSTAMP:20260423T040003Z
UID:OWNS/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/18/">Fi
 niteness and periodicity of continued fractions over quadratic number fiel
 ds</a>\nby Francesco Veneziano (University of Genova) as part of One World
  Numeration seminar\n\n\nAbstract\nWe consider continued fractions with pa
 rtial quotients in the ring of integers of a quadratic number field $K$\; 
 a particular example of these continued fractions is the $\\beta$-continue
 d fraction introduced by Bernat. We show that for any quadratic Perron num
 ber $\\beta$\, the $\\beta$-continued fraction expansion of elements in $\
 \mathbb{Q}(\\beta)$ is either finite of eventually periodic. We also show 
 that for certain four quadratic Perron numbers $\\beta$\, the $\\beta$-con
 tinued fraction represents finitely all elements of the quadratic field $\
 \mathbb{Q}(\\beta)$\, thus answering questions of Rosen and Bernat. \nBase
 d on a joint work with Zuzana Masáková and Tomáš Vávra.\n
LOCATION:https://researchseminars.org/talk/OWNS/18/
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