Result: On Kummer-Type Congruences for Derivatives of Barnes' Multiple Bernoulli Polynomials: On Kummer-type congruences for derivatives of Barnes' multiple Bernoulli polynomials
Title:
On Kummer-Type Congruences for Derivatives of Barnes' Multiple Bernoulli Polynomials: On Kummer-type congruences for derivatives of Barnes' multiple Bernoulli polynomials
Authors:
Source:
Journal of Number Theory. 92:1-36
Publisher Information:
Elsevier BV, 2002.
Publication Year:
2002
Subject Terms:
derivative of Barnes' multiple Bernoulli polynomial, Algebra and Number Theory, Barnes' multiple zeta function, Bernoulli polynomials, Kummer congruence, Kummer congruences, JFM 35.0462.01, p-adic interpolation, 0101 mathematics, Bernoulli and Euler numbers and polynomials, Other Dirichlet series and zeta functions, 01 natural sciences
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
0022-314X
DOI:
10.1006/jnth.2001.2702
Access URL:
Rights:
Elsevier Non-Commercial
Accession Number:
edsair.doi.dedup.....1f907a9898e4b85d18d07034ac44f00d
Database:
OpenAIRE
Further Information
\textit{E. W. Barnes} [Trans. Camb. Philos. Soc. 19, 374-425 (1904; JFM 35.0462.01)] introduced a version of the multiple zeta function, and also a system of Bernoulli-type polynomials. The values of Barnes' zeta at negative integers are expressed via the first derivatives of the Bernoulli-Barnes polynomials (the above functions are functions of one complex variable depending on several parameters). The author shows that the first derivatives of the Bernoulli-Barnes polynomials satisfy congruences generalizing the classical Kummer congruences for the Bernoulli polynomials. An interpretation in terms of \(p\)-adic integrals is given.