Generalized Carlitz's \(q\)-Bernoulli numbers in the \(p\)-adic number field (Q2729681)
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scientific article; zbMATH DE number 1623203
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Generalized Carlitz's \(q\)-Bernoulli numbers in the \(p\)-adic number field |
scientific article; zbMATH DE number 1623203 |
Statements
29 October 2001
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\(q\)-Bernoulli number
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Kummer congruence
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\(q\)-Bernoulli measure
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0.95832586
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0.93175817
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0.91352373
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0.9133629
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Generalized Carlitz's \(q\)-Bernoulli numbers in the \(p\)-adic number field (English)
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It was shown by the authors [Bull. Aust. Math. Soc. 62, No. 2, 227--234 (2000; Zbl 0959.11012), and T. Kim, J. Number Theory 76, No. 2, 320--329 (1999; Zbl 0941.11048)] that Carlitz's \(q\)-Bernoulli numbers can be represented via a \(q\)-analogue of the \(p\)-adic Volkenborn integral. That has led to the definitions of the generalized Carlitz's \(q\)-Bernoulli numbers and the extended \(q\)-Bernoulli polynomials.NEWLINENEWLINEIn the paper under review the above approach is employed for obtaining some identities for the generalized Carlitz's \(q\)-Bernoulli numbers. A Kummer-type congruence is proved.
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