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SUMMARY:Julie Wang (Academia Sinica)
DTSTART:20200604T000000Z
DTEND:20200604T005000Z
DTSTAMP:20260421T084601Z
UID:NTOC2020/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTOC2020/6/"
 >On Pisot’s d-th root conjecture for function fields and related GCD est
 imates</a>\nby Julie Wang (Academia Sinica) as part of Number Theory Onlin
 e Conference 2020\n\n\nAbstract\nLet $B(X)=\\sum_{n=0}^{\\infty}b(n)X^n$ r
 epresent a rational function in $\\mathbb Q(X)$ \n  and suppose that  $b(n
 )$ is a perfect $d$-th power for all large $n\\in\\mathbb N$. Pisot's  $d$
 -th root conjecture states that one can choose a $d$-th root $a(n)$ of $b(
 n)$ such that $A(X):=\\sum a(n)X^n$ is again a rational function. In this 
 talk\,  we propose a function-field analog of Pisot's $d$-th root conjectu
 re  and prove it under some ``non-triviality''\nassumption.  We relate the
  problem to a  result of Pasten-Wang  on Buchi's $d$-th power problem and 
  develop  a function-field analog of an GCD estimate in a recent work of L
 evin-Wang.      This is a joint work with Ji Guo and Chia-Liang Sun.\n
LOCATION:https://researchseminars.org/talk/NTOC2020/6/
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