ULethbridge Number Theory and Combinatorics Seminar: Dang-Khoa Nguyen

A power series f(x1,…,xm)∈C[[x1,…,xm]] is said to be D-finite if all the partial derivatives of f span a finite dimensional vector space over the field C(x1,…,xm). For the univariate series f(x)=∑anxn, this is equivalent to the condition that the sequence (an) is P-recursive meaning a non-trivial linear recurrence relation of the form:

Pd(n)an+d+⋯+P0(n)an=0

where the Pi'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. This is from a joint work with Jason Bell and Umberto Zannier in 2019 and a more recent work in June 2022.