JP Journal of Algebra, Number Theory and Applications
Volume 15, Issue 1, Pages 29 - 44
(October 2009)
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BERNOULLI NUMBERS ATTACHED TO p-ADIC FUNCTIONS AND A VON STAUDT-CLAUSEN TYPE THEOREM
Ken Kamano (Japan)
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Abstract: As a generalization of the ordinary Bernoulli numbers, we define Bernoulli numbers attached to p-adic functions by using a p-adic integral. We introduce semi-analytic functions on the ring of p-adic integers, and prove that Bernoulli numbers attached to semi-analytic functions satisfy a von Staudt-Clausen type theorem. |
Keywords and phrases: Bernoulli numbers, von Staudt-Clausen theorem, p-adic integral. |
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