Congruences for coefficients of rational functions

par Frits Beukers (Universiteit Utrecht)

mardi 19 déc. 2017, 10:45 → 11:45 Europe/Paris

Bât. Braconnier, salle Fokko du Cloux (ICJ, Université Lyon 1)

We discuss generalizations of the well-known congruences u(mp^r) = u(mp^(r-1)) mod p^r of the Lucas sequence u(0)=2, u(1)=1, u(2)=3, u(3)=4, ... Here m,r are arbitrary positive integers and p is an arbitrary prime. The generating function of the u(n) is (x+2x^2)/(1-x-x^2). It turns out that similar congruences occur for coefficients of certain multivariable rational functions. We explore this phenomenon. The ultimate goal will be to find cases where congruences mod p^(2r) and p^(3r) hold.