# On Bernoulli identities and applications.

• Volume: 14, Issue: 1, page 167-213
• ISSN: 0213-2230

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## Abstract

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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. Kummer's congruences play important roles in the investigation of p-adic interpolation of the classical Riemann zeta function (...).

## How to cite

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Eie, Minking, and Lai, King F.. "On Bernoulli identities and applications.." Revista Matemática Iberoamericana 14.1 (1998): 167-213. <http://eudml.org/doc/39544>.

@article{Eie1998,
abstract = {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. Kummer's congruences play important roles in the investigation of p-adic interpolation of the classical Riemann zeta function (...).},
author = {Eie, Minking, Lai, King F.},
journal = {Revista Matemática Iberoamericana},
keywords = {Función zeta; Números de Bernoulli; Congruencia; Bernoulli numbers; von Staudt-Clausen theorem; zeta function; Kummer congruence; -adic interpolation},
language = {eng},
number = {1},
pages = {167-213},
title = {On Bernoulli identities and applications.},
url = {http://eudml.org/doc/39544},
volume = {14},
year = {1998},
}

TY - JOUR
AU - Eie, Minking
AU - Lai, King F.
TI - On Bernoulli identities and applications.
JO - Revista Matemática Iberoamericana
PY - 1998
VL - 14
IS - 1
SP - 167
EP - 213
AB - 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. Kummer's congruences play important roles in the investigation of p-adic interpolation of the classical Riemann zeta function (...).
LA - eng
KW - Función zeta; Números de Bernoulli; Congruencia; Bernoulli numbers; von Staudt-Clausen theorem; zeta function; Kummer congruence; -adic interpolation
UR - http://eudml.org/doc/39544
ER -

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