# Generalized Volkenborn Integrals Associated with p -Adic Distributions and the Bernoulli Numbers

## 抄録

Abstract: Our goal is to give a formula representing the Bernoulli numbers by p-adic distributions. We consider p-adic distributions on the ring of p-adic integers which are invariant by rotations around the origin, and define a generalization of the Vokenborn integrals with respect to such distributions. It is shown the generalized Volkenborn integrals of power functions, and of negative powers of the p-adic norm converge under some conditions on the distributions, and their universal relation to the Bernoulli numbers is presented.

本文言語 English 164-171 8 P-Adic Numbers, Ultrametric Analysis, and Applications 14 2 https://doi.org/10.1134/S2070046622020078 Published - 2022 6月

• 数学 (全般)

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