Arithmetic properties of Apéry-like numbers

Speaker: Eric Delaygue, Lyon

Date: Monday, April 13th

Time: 4:00pm

Location:  Seminar Room, Ag 1.01

Abstract:

In his proof of the irrationality of the Riemann zeta function evaluated at 3, Apéry used a sequence of integers satisfying many classic congruences. In particular, Gessel proved that this sequence satisfies Lucas congruences for every prime. By using these congruences and the recurrence relation satisfied by Apéry numbers, I will prove a conjecture of Beukers on the divisibility of these numbers by prime powers. I will prove similar results for classic numbers such as Domb, Franel numbers and constant terms of powers of certain Laurent polynomials.


Series: Analysis and Number Theory