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SUMMARY:Kelly Isham (University of California Irvine)
DTSTART:20210603T210000Z
DTEND:20210603T220000Z
DTSTAMP:20260423T022807Z
UID:UCSD_NTS/40
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSD_NTS/40/
 ">Asymptotic growth of orders in a fixed number field via subrings in $\\m
 athbb{Z}^n$</a>\nby Kelly Isham (University of California Irvine) as part 
 of UCSD number theory seminar\n\nLecture held in normally APM 7321\, curre
 ntly online.\n\nAbstract\nLet $K$ be a number field of degree $n$ and $\\m
 athcal{O}_K$ be its ring of integers. An order in $\\mathcal{O}_K$ is a fi
 nite index subring that contains the identity. A major open question in ar
 ithmetic statistics asks for the asymptotic growth of orders in $K$. In th
 is talk\, we will give the best known lower bound for this asymptotic grow
 th. The main strategy is to relate orders in $\\mathcal{O}_K$ to subrings 
 in $\\mathbb{Z}^n$ via zeta functions. Along the way\, we will give lower 
 bounds for the asymptotic growth of subrings in $\\mathbb{Z}^n$ and for th
 e number of index $p^e$ subrings in $\\mathbb{Z}^n$. We will also discuss 
 analytic properties of these zeta functions.\n\nThere will be a pretalk at
  1:30 Pacific time.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/40/
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