The Universal Von Staudt Theorems
- 1 October 1989
- journal article
- research article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 315 (2) , 591-603
- https://doi.org/10.2307/2001296
Abstract
We prove general forms of von Staudt's theorems on the Bernoulli numbers. As a consequence we are able to deduce strong versions of a number of congruences involving various generalisations of the Bernoulli numbers. For example we obtain an improved form of a congruence due to Hurwitz involving the Laurent series coefficients of the Weierstrass elliptic function associated with a square lattice.Keywords
This publication has 9 references indexed in Scilit:
- Combinatorial and arithmetic identities based on formal group lawsLecture Notes in Mathematics, 1987
- Extensions of umbral calculus: Penumbral coalgebras and generalised Bernoulli numbersAdvances in Mathematics, 1986
- An analogue of the Von Staudt-Clausen theoremJournal of Algebra, 1984
- A concept of Bernoulli numbers in algebraic function fields.Journal für die reine und angewandte Mathematik (Crelles Journal), 1979
- Advanced CombinatoricsMathematics of Computation, 1976
- The congruences of Clausen — von Staudt and Kummer for Bernoulli-Hurwitz numbersMathematische Annalen, 1975
- A Property of the Bernoulli NumbersThe American Mathematical Monthly, 1959
- Some Congruences for the Bernoulli NumbersAmerican Journal of Mathematics, 1953
- The coefficients of the reciprocal of a seriesDuke Mathematical Journal, 1941