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Séminaire Combinatoire et Théorie des Nombres ICJ

Congruences for coefficients of rational functions

by Frits Beukers (Universiteit Utrecht)

mardi 19 décembre 2017 de au (Europe/Paris)
at ICJ, Université Lyon 1 ( Bât. Braconnier, salle Fokko du Cloux )
Description
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.