On the polynomial part of a restricted partition function

Karl Dilcher (Dalhousie University, Halifax, Canada)
December 21, 2017 — 10:30 — "Salle du conseil du L2S"

Abstract

We prove an explicit formula for the polynomial part of a restricted partition function, also known as the first Sylvester wave. This is achieved by way of some identities for higher-order Bernoulli polynomials, one of which is analogous to Raabe’s well-known multiplication formula for the ordinary Bernoulli polynomials. As a consequence of our main result we obtain an asymptotic expression of the first Sylvester wave as the coefficients of the restricted partition grow arbitrarily large. (Joint work with Christophe Vignat).