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Summary: UNIVERSAL BERNOULLI POLYNOMIALS AND P-ADIC
CONGRUENCES
ABSTRACT. We de ne universal arbitrary order Bernoulli polynomials which
generalize the classical ones. We determine the succession of p-adic 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
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1. INTRODUCTION
The classical Bernoulli numbers B n are de ned by
t
e t 1 =
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