DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

Co-organizers:

Andrew Baxter, Rutgers University, baxter{at} math [dot] rutgers [dot] edu

Lara Pudwell, Rutgers University, lpudwell {at} math [dot] rutgers [dot] edu

Doron Zeilberger, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: p-adic pictures from irresistible sequences

Speaker: Victor Moll, Tulane University

Date: Thursday, November 29, 2007 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

Legendre's formula ν_p(n!)=(n-s_p(n))/(p-1) is the simplest instance of the p-adic valuation for a sequence defined by a first order recurrence t_n=Q(n)t_n-1. Here Q is a polynomial with integer coefficients and s_p(n) is the sum of the digits of n in base p.

In this talk we describe the asymptotics of ν_p(t_n) as n → ∞

The extension to the case t_n=Q₁(n)t_n-1+Q₂(n)t_n-2 will be illustrated with the p-adic valuation of the Stirling numbers.

Joint work with T. Amdeberhan, Dante Manna and Luis Medina.