 
Summary: UNIVERSAL BERNOULLI POLYNOMIALS AND PADIC
CONGRUENCES
ABSTRACT. We dene universal arbitrary order Bernoulli polynomials which
generalize the classical ones. We determine the succession of padic poles of
their coeÆcients, and generalize our previous results as well as results of Car
litz and Kummer for positive integer order Bernoulli numbers and values of
ordinary Bernoulli polynomials respectively.
Arnold Adelberg
Department of Mathematics
Grinnell College
Grinnell, IA 50112
adelbe@math.grinnell.edu
Key Words. Bernoulli Polynomials and Numbers, Kummer Congruences,
Newton Polygons
1
1. INTRODUCTION
The classical Bernoulli numbers B n are dened by
t
e t 1 =
