Summary: KUMMER CONGRUENCES FOR
UNIVERSAL BERNOULLI NUMBERS
AND RELATED CONGRUENCES FOR
POLY-BERNOULLI NUMBERS
Arnold Adelberg
Grinnell College
Department of Mathematics
Grinnell, Iowa 50112
USA
adelbe@math.grin.edu

Abstract
We rene our proof of the Kummer congruences for the universal
Bernoulli numbers ^
B n to include the case where n  1 (mod p 1).
We also use polylogarithm series to dene universal poly-Bernoulli
numbers of index k, and we prove universal von Staudt type congru-
ences for these numbers, which strengthen and simplify the congru-
ences for the classical poly-Bernoulli numbers.
AMS Subject Classications: 11B68, 11B83

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

Collections: Mathematics