Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
 

Summary: PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 136, Number 1, January 2008, Pages 6171
S 0002-9939(07)09025-9
Article electronically published on August 14, 2007
BOUNDS OF DIVIDED UNIVERSAL BERNOULLI NUMBERS
AND UNIVERSAL KUMMER CONGRUENCES
ARNOLD ADELBERG, SHAOFANG HONG, AND WENLI REN
(Communicated by Wen-Ching Winnie Li)
Abstract. Let p be a prime. We obtain good bounds for the p-adic sizes of the
coefficients of the divided universal Bernoulli number
^Bn
n
when n is divisible
by p - 1. As an application, we give a simple proof of Clarke's 1989 universal
von Staudt theorem. We also establish the universal Kummer congruences
modulo p for the divided universal Bernoulli numbers for the case (p - 1)|n,
which is a new result.
1. Introduction
There are many beautiful and useful congruences in number theory. Some ex-

  

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

 

Collections: Mathematics