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SUMMARY:Wadim Zudilin (Radboud University\, Nijmegen)
DTSTART:20201123T121500Z
DTEND:20201123T131500Z
DTSTAMP:20260423T022931Z
UID:WarsawNT/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WarsawNT/13/
 ">Dwork-type ($q$-)(super)congruences</a>\nby Wadim Zudilin (Radboud Unive
 rsity\, Nijmegen) as part of Warsaw Number Theory Seminar\n\nLecture held 
 in room 403 at IMPAN.\n\nAbstract\nThe "microscope" principle is this: If 
 a rational function A(q) of variable q vanishes at every p-th root of unit
 y (for p prime)\, then A(q) == 0 modulo Φ_p(q)\, the p-th cyclotomic poly
 nomial\; assuming that A(1) is a well-defined rational number with a p-fre
 e denominator and specialising the congruence at q=1 we conclude with A(1)
  == 0 modulo p.\nIn other words\, behaviour of rational functions at p-th 
 roots of unity may be instructive for gaining information about their valu
 es at 1 modulo p. With some "creative" extras\, we can further consider di
 visibility by higher powers of primes (and we can even deal with not neces
 sarily primes).\nIn my talk\, partly based on recent joint work with Victo
 r Guo\, I plan to highlight some novel outcomes of this "creative microsco
 pe" methodology -- examples of Dwork-type supercongruences for truncated h
 ypergeometric sums.\n
LOCATION:https://researchseminars.org/talk/WarsawNT/13/
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