Summary: This is a condensed version of the full paper, containing the complete Introduction, all
statements of Lemma, Theorems, and Corollaries, some of the Remarks, and the Bibliog­
raphy. The full version can be obtained from the author.
Arithmetic properties of the N¨orlund polynomial B (x)
n
Arnold Adelberg
Dedicated to H. W. Gould on the occasion of his 70th birthday.
Abstract
For any prime p we establish a congruence of Kummer type for the N¨orlund polynomial
B (x)
n , and determine the highest power of p which divides the coefficient denominators of
the N¨orlund polynomial. This improves the result of [4] where only an upper bound was
proven. We deduce a simple formula for the least common denominator of the coefficients.
Applications are made for the Stirling polynomials.
Keywords N¨orlund polynomials, Bernoulli numbers and polynomials, Stirling polynomi­
als, Kummer congruences.
1. Introduction
We are pleased to contribute to this volume dedicated to H. W. Gould, whose collection
of binomial identities [6] led us into the field of Bernoulli and related polynomials [2].
The N¨orlund polynomials B (x)

Source: Adelberg, Arnold - Department of Mathematics and Computer Science, Grinnell College

Collections: Mathematics