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SUMMARY:Dang-Khoa Nguyen (University of Calgary)
DTSTART:20220926T180000Z
DTEND:20220926T190000Z
DTSTAMP:20260423T035534Z
UID:NTC/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTC/1/">Heig
 ht gaps for coefficients of D-finite power series</a>\nby Dang-Khoa Nguyen
  (University of Calgary) as part of Lethbridge number theory and combinato
 rics seminar\n\nLecture held in University of Lethbridge\, room M1040 (Mar
 kin Hall).\n\nAbstract\nA power series $f(x_1\,\\ldots\,x_m)\\in \\mathbb{
 C}[[x_1\,\\ldots\,x_m]]$ is said to be D-finite if all the partial derivat
 ives of $f$\n	span a finite dimensional vector space over\n	the field $\\m
 athbb{C}(x_1\,\\ldots\,x_m)$. For the univariate series $f(x)=\\sum a_nx^n
 $\, this is equivalent to the condition that the sequence $(a_n)$ is P-rec
 ursive meaning a non-trivial linear recurrence relation of the form:\n	$$P
 _d(n)a_{n+d}+\\cdots+P_0(n)a_n=0$$\n	where the $P_i$'s are polynomials. In
  this talk\, we consider D-finite power series with algebraic coefficients
  and discuss the growth of the Weil height of these coefficients.\n	\n		\n
 	This is from a joint work with Jason Bell and Umberto Zannier in 2019 and
  a more recent work in June 2022.\n
LOCATION:https://researchseminars.org/talk/NTC/1/
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