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DTSTAMP:20250802T083142Z
DESCRIPTION:Title: On the metric theory of approximations by reduced fracti
 ons.\n\nAbstract: In 2019 Dimitris Koukoulopoulos and James Maynard solved
  the Duffin-Schaeffer conjecture\, a central problem in metric Diophantine
  approximation that had been open since 1941. Very roughly speaking\, the 
 Koukoulopoulos-Maynard theorem states that there is a simple convergence/d
 ivergence criterion which allows to decide whether (Lebesgue-)almost all r
 eal numbers allow infinitely many coprime rational approximations of a cer
 tain quality\, or not. In this talk I will report on very recent joint wor
 k with Bence Borda and Manuel Hauke (both from TU Graz as well) which goes
  beyond the existence of infinititely many solutions\, and gives an actual
  asymptotics for the typical number of coprime rational approximations up 
 to a certain threshold in the divergence case. I will relate some of the h
 istory of the subject\, and try to convey some of the (probablistic) philo
 sophy behind the problem. The proof relies mainly on sieve theory and the 
 'anatomy of integers'\, and in particular on the method of GCD graphs whic
 h was introduced by Koukoulopoulos-Maynard in their proof.\n\n \n\n \n\nEn
  ligne/Web - Pour information\, veuillez communiquer à/For details\, pleas
 e contact: martinez [at] crm.umontreal.ca\n
DTSTART:20220421T190000Z
DTEND:20220421T203000Z
SUMMARY:Christophe Aistleitner\, Graz
URL:/mathstat/channels/event/christophe-aistleitner-gr
 az-339115
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