BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Nathan McNew (Towson University)
DTSTART:20250523T210000Z
DTEND:20250523T212500Z
DTSTAMP:20260423T041812Z
UID:CANT2025/59
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/59/
 ">The density of covering numbers</a>\nby Nathan McNew (Towson University)
  as part of Combinatorial and additive number theory (CANT 2025)\n\nLectur
 e held in CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\n
 In 1950\, Erd\\H{o}s introduced covering systems--finite collections of ar
 ithmetic progressions whose union contains every integer. They featured in
  some of his favorite problems\, many of which are still open.  In 1979\,
  answering one of Erd\\H{o}s's questions\, Haight introduced covering numb
 ers: positive integers $n$ for which a covering system can be constructed 
 with distinct moduli that are divisors of $n$. If no proper divisor of $n$
  is a covering number\, we call $n$ a primitive covering number.  We esta
 blish an upper bound on the number of primitive covering numbers\, from wh
 ich it follows that the set of covering numbers has a natural density. By 
 refining techniques used to bound the density of abundant numbers\, we obt
 ain relatively tight bounds for the density of covering numbers and\, in t
 he process\, improve the bounds on the density of abundant numbers as well
 .\n
LOCATION:https://researchseminars.org/talk/CANT2025/59/
END:VEVENT
END:VCALENDAR