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