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SUMMARY:Nathan McNew (Towson University)
DTSTART:20200603T180000Z
DTEND:20200603T182500Z
DTSTAMP:20260423T011218Z
UID:CANT2020/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/37/
 ">Primitive sets in function fields</a>\nby Nathan McNew (Towson Universit
 y) as part of Combinatorial and additive number theory (CANT 2021)\n\n\nAb
 stract\nA set of integers is \\emph{primitive} if no element divides anoth
 er.  \nErdős showed that $f(A) = \\sum_{a \\in A}\\frac{1}{a\\log a}$ con
 verges for any primitive set $A$ of integers \ngreater than one\, and late
 r conjectured this sum is maximized when $A$ is the set $P_1$ of primes.  
 \nBanks and Martin further conjectured that  \n$f(\\mathcal{P}_1) > \\ldot
 s > f(\\mathcal{P}_k) > f(\\mathcal{P}_{k+1}) > \\ldots$\, \nwhere $\\math
 cal{P}_j$ denotes the integers with exactly $j$ prime factors. \nHowever\,
  this was recently disproven by Lichtman.  \nWe consider the analogous que
 stions for polynomials over a finite field $\\mathbb{F}_q[x]$\, \nobtainin
 g bounds on the analogous sum\, and find that while the analogue of the Ba
 nks and Martin \nconjecture similarly fails for small values of $q$\, it s
 eems likely to hold for larger values.  \n\nJoint work with Andrés Gómez
 -Colunga\, Charlotte Kavaler and Mirilla Zhu.\n
LOCATION:https://researchseminars.org/talk/CANT2020/37/
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