On Kummer-Type Congruences for Derivatives of Barnes' Multiple Bernoulli Polynomials

The theorem of Kummer congruences of Bernoulli numbers says that if p−1∤m and m≡n (modpN(p−1)), then(1−pm−1)Bmm≡(1−pn−1)Bnn(modpN+1). In this paper we generalize these congruences to derivatives of Barnes' multiple Bernoulli polynomials by an elementary method and give a p-adic interpretation o...

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Bibliographic Details
Published in:Journal of number theory 2002-01, Vol.92 (1), p.1-36
Main Author: Ota, Kaori
Format: Article
Language:English
Subjects:
Barnes' multiple zeta function
derivative of Barnes' multiple Bernoulli polynomial
Kummer congruence
p-adic interpolation
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Summary:The theorem of Kummer congruences of Bernoulli numbers says that if p−1∤m and m≡n (modpN(p−1)), then(1−pm−1)Bmm≡(1−pn−1)Bnn(modpN+1). In this paper we generalize these congruences to derivatives of Barnes' multiple Bernoulli polynomials by an elementary method and give a p-adic interpretation of them.
ISSN:0022-314X
1096-1658
DOI:10.1006/jnth.2001.2702