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DTSTART:20240310T070000
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DTSTART;TZID=America/Toronto:20250305T130000
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URL:https://uwaterloo.ca/pure-mathematics/events/student-number-theory-semi
 nar-77
SUMMARY:Student Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:JÉRÉMY CHAMPAGNE\, UNIVERSITY OF WATERLOO\n\nEquidistribution
  and the probability of coprimality of some integer\ntuples\n\n\" What is
  the probability of two random integers being coprime? \"\n\nThis questio
 n\, sometimes called \" Chebyshev’s Problem »\, is very\nnatural and 
 happens to have a very straightforward answer. Using only\nelementary meth
 ods\, one can easily show that the natural density of\npairs (m\,n) with g
 cd(m\,n)=1 is exactly 1/zeta(2)=6/pi^2=60.8..%.\n\nKnowing this\, one migh
 t seek certain g:N->N for which the density of\nn’s with gcd(n\, g(n))=1
  is also 1/zeta(2)\, which give a certain\nsense of randomness to the func
 tion g. Many functions with that\nproperty can be found in the literature\
 , and we have a special\ninterest for those of the form g(n)=[f(n)] where 
 f is a real valued\nfunction with some equidistributive properties modulo 
 one\; for\nexample\, Watson showed in 1953 that g(n)=[αn] has this proper
 ty\nwhenever α is irrational. In this talk\, we use a method of Spilker t
 o\nobtain a more general framework on what properties f(n) must have\, and
 \nalso what conditions can replace coprimality of integer pairs.\n\nMC 540
 3
DTSTAMP:20260504T161325Z
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