# On Bernoulli identities and applications.

Revista Matemática Iberoamericana (1998)

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

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topEie, 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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