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SUMMARY:Abbas Maarefparvar (University of Lethbridge)
DTSTART:20231107T210000Z
DTEND:20231107T220000Z
DTSTAMP:20260423T035412Z
UID:NTC/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTC/32/">Som
 e Pólya fields of small degrees</a>\nby Abbas Maarefparvar (University of
  Lethbridge) as part of Lethbridge number theory and combinatorics seminar
 \n\nLecture held in University of Lethbridge: M1060 (Markin Hall).\n\nAbst
 ract\nHistorically\, the notion of Pólya fields dates back to some works 
 of George Pólya and Alexander Ostrowski\, in 1919\, on entire functions w
 ith integervalues at integers\; a number field $K$ with ring of  integers 
 $\\mathcal{O}_K$ is  called a Pólya field whenever the $\\mathcal{O}_K$-m
 odule $\\{ f \\in K[X]  : f(\\mathcal{O}_K ) \\subseteq \\mathcal{O}_K \\}
 $ admits an $\\mathcal{O}_K$-basis with exactly one member from each degre
 e. Pólya fields can be thought of as a generalization of number fields wi
 th class number one\, and their classification of a specific degree has be
 come recently an active research subject in algebraic number theory. In th
 is talk\, I will present some criteria for $K$ to be a Pólya field. Then 
 I will give some results concerning Pólya fields of degrees $2\, 3$\, and
  $6$.\n
LOCATION:https://researchseminars.org/talk/NTC/32/
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