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DTSTART:20240310T070000
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DTSTART:20241103T060000
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DTSTART;TZID=America/Toronto:20241105T102000
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URL:https://uwaterloo.ca/pure-mathematics/events/number-theory-seminar-131
SUMMARY:Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:SUNIL NAIK\, QUEEN'S UNIVERSITY\n\nOn a question of Christensen
 \, Gipson and Kulosman\n\nThe study of irreducible polynomials in various 
 polynomial rings is an\nimportant topic in mathematics. In this context\, 
 polynomials with\nrestricted exponents have become the focus of considerab
 le attention\nin recent years. Motivated by these considerations\, Matsuda
  introduced\nthe ring $F[X\;M]$ of polynomials with coefficients in a fiel
 d $F$ and\nexponents in a commutative\, torsion-free\, cancellative (addit
 ive)\nmonoid $M$ and began an inquiry into the irreducibility of various\n
 polynomials in these rings. For any prime $\\ell$\, we say that $M$ is a\n
 Matsuda monoid of type $\\ell$ if for each indivisible $\\alpha$ in $M$\,\
 nthe polynomial $X^{\\alpha}-1$ is irreducible in $F[X\;M]$ for any field\
 n$F$ of characteristic $\\ell$.\n\nLet $M$ be the additive submonoid of no
 n-negative integers generated\nby 2 and 3. In a recent work\, Christensen\
 , Gipson\, and Kulosman proved\nthat $M$ is not a Matsuda monoid of type 2
  and type 3 and they have\nraised the question of whether $M$ is a Matsuda
  monoid of type $\\ell$\nfor any prime $\\ell$. Assuming the Generalized R
 iemann Hypothesis\n(GRH)\, Daileda showed that $M$ is not a Matsuda monoid
  of any positive\ntype. In this talk\, we will discuss an unconditional pr
 oof of the\nabove result using its connection with Artin’s primitive roo
 t\nconjecture.
DTSTAMP:20260407T211622Z
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