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

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


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

In this talk we describe the asymptotics of νp(tn) as n → ∞

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

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