Generalized Kummer Congruences
by
Paul T. Young
College of Charleston

Kummer's congruences for the Bernoulli numbers have been generalized and strengthened in many ways. In this paper we consider two of the strongest forms of these congruences, and begin with a general theorem on sequences which exhibit analogous congruences. We then demonstrate generalizations of Kummer congruences for values of Bernoulli polynomials and generalized Bernoulli polynomials. These values interpolate values of Hurwitz zeta functions and two-variable p-adic L-functions. We also give a general theorem on Kummer congruences for degenerate sequences.

Date received: April 16, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacu-11.