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Transactions of the American Mathematical Society

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The universal von Staudt theorems

Author: Francis Clarke
Journal: Trans. Amer. Math. Soc. 315 (1989), 591-603
MSC: Primary 11B68; Secondary 05A19, 12E10, 33A25
MathSciNet review: 986687
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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.

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Keywords: Bernoulli numbers
Article copyright: © Copyright 1989 American Mathematical Society