BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dang-Khoa Nguyen (University of Calgary) DTSTART:20220926T180000Z DTEND:20220926T190000Z DTSTAMP:20260404T150745Z UID:NTC/1 DESCRIPTION:Title: Height gaps for coefficients of D-finite power series\nby Dang-Khoa Nguyen (University of Calgary) as part of Lethbridge number theory and co mbinatorics seminar\n\nLecture held in University of Lethbridge\, room M10 40 (Markin 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 derivatives of $f$\n span a finite dimensional vector space over\n the fie ld $\\mathbb{C}(x_1\,\\ldots\,x_m)$. For the univariate series $f(x)=\\sum a_nx^n$\, this is equivalent to the condition that the sequence $(a_n)$ i s P-recursive 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 polynomi als. In this talk\, we consider D-finite power series with algebraic coeff icients 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 2 019 and a more recent work in June 2022.\n LOCATION:https://stable.researchseminars.org/talk/NTC/1/ END:VEVENT END:VCALENDAR