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Remark on p-adic and q-Bernoulli numbers. (English) Zbl 0993.11006

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.

Note that there exists another sequence β k (q) of q-Bernoulli numbers [introduced by L. Carlitz, Duke Math. J. 15, 987-1000 (1948; Zbl 0032.00304)]. The corresponding p-adic q-L-functions were found by N. Koblitz [J. Number Theory 14, 332-339 (1982; Zbl 0501.12020)].

MSC:
11B68Bernoulli and Euler numbers and polynomials
11S80Other analytic theory of local fields
05A30q-calculus and related topics