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Revista Matemática Iberoamericana

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Volume 14, Issue 1, 1998, pp. 167–213
DOI: 10.4171/RMI/239

Published online: 1998-04-30

On Bernoulli identities and applications

Minking Eie[1] and King F. Lai[2]

(1) National Chung Cheng University, Chia-Yi, Taiwan
(2) The University of Sydney, Australia

Bernoulli numbers appear as special values of zeta functions at integers and identities relating the Bernoulli numbers follow as a consequence of properties of the corresponding zeta functions. The most famous example is that of the special values of the Riemann zeta function and the Bernoulli identities due to Euler. In this paper we introduce a general principle for producing Bernoulli identities and apply it to zeta functions considered by Shintani, Zagier and Eie. Our results include some of the classical results of Euler and Ramanujan. Kummers congruences play important roles in the investigation of $p$-adic interpolation of the classical Riemann zeta function.

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Eie Minking, Lai King: On Bernoulli identities and applications. Rev. Mat. Iberoam. 14 (1998), 167-213. doi: 10.4171/RMI/239