Speaker:
Jason Bell, Simon Fraser University
Abstract:
Let F(x) be a power series with integer coefficients that satisfies a non-trivial linear homogeneous differential equation. We consider the set of natural numbers n for which the coefficients f(n)=0 and the set of natural numbers n for which f(n)=0 modulo a prime p. We show that many interesting links to finite-state automata, diagonals of rational functions, and to Diophantine problems arise in the study of these questions and we survey both what is known and what is conjectured to be true in general.