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DTSTART:20250309T070000
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DTSTART:20251102T060000
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DTSTART;TZID=America/Toronto:20251107T110000
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URL:https://uwaterloo.ca/pure-mathematics/events/student-number-theory-semi
 nar-90
SUMMARY:Student Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:JÉRÉMY CHAMPAGNE\, UNIVERSITY OF WATERLOO\n\n_Small fractiona
 l parts of polynomials (aka 11J54)_\n\nIn the eary 1900's\, Hardy and Litt
 lewood asked the following question:\ngiven a real number α and integer k
 >1\, what is the smallest distance\nobtained between αn^k and the nearest
  integer as n runs over the set\n{1\,...\,N}? More specifically\, does the
 re exist an exponent theta_k>0\nsuch that the smallest distance is at most
  N^-theta_k for sufficiently\nlarge N? This question was answered positive
 ly by Vinogradov a couple\ndecades later\, but the question of finding the
  largest possible\ntheta_k with this property is still open.\n\nIn this ta
 lk\, I will discuss some historical results around this\nproblem and prese
 nt some typical methods used in the literature.\n\nMC 5479
DTSTAMP:20260502T041344Z
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