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Zbl 0993.11006
Kim, Taekyun; Kim, Han Soo
Remark on $p$-adic and $q$-Bernoulli numbers. (English)
[J] Adv. Stud. Contemp. Math., Pusan 1, 127-136 (1999). ISSN 1229-3067

In an earlier paper [Rep. Fac. Sci. Eng., Saga Univ., Math. 23, 1-7 (1995; Zbl 0820.11071)] the authors introduced a $p$-adic $q$-integral giving an integral representation of the $q$-Bernoulli numbers $B_k(q)$. Now this approach is used for defining $q$-Bernoulli polynomials. Then the $p$-adic $q$-Bernoulli measures are constructed and used to define $p$-adic $q$-$L$-series, which interpolate $q$-Bernoulli numbers. \par Note that there exists another sequence $\beta_k(q)$ of $q$-Bernoulli numbers [introduced by {\it L. Carlitz}, Duke Math. J. 15, 987-1000 (1948; Zbl 0032.00304)]. The corresponding $p$-adic $q$-$L$-functions were found by {\it N. Koblitz} [J. Number Theory 14, 332-339 (1982; Zbl 0501.12020)].
[Anatoly N.Kochubei (Ky\" iv)]

MSC 2000:: *11B68 Bernoulli numbers, etc.
11S80 Other analytic theory of local fields
05A30 q-calculus and related topics

Keywords: $q$-Bernoulli numbers; $q$-Bernoulli polynomials; $p$-adic $q$-$L$-functions

Citations: Zbl 0820.11071; Zbl 0032.00304; Zbl 0501.12020

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