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On modification of the $$q$$-$$L$$-series and its applications. (English) Zbl 1025.11030
In an earlier paper [Proc. Japan Acad., Ser. A 75, 23–25 (1999; Zbl 0931.11031)] the author introduced a version of the $$q$$-Riemann $$\zeta$$-function. Now he extends his results introducing and studying the $$q$$-Hurwitz $$\zeta$$-function and $$q$$-$$L$$-series (for another approach see J. Satoh [J. Number Theory 31, 346–362 (1989; Zbl 0675.12010)]). For $$q\to 1$$, some relations for the ordinary Dirichlet $$L$$-series are obtained. In particular, a new proof is given for Katsurada’s formula for the values of the Dirichlet $$L$$-series at positive integers [M. Katsurada, Acta Arith. 90, 79–89 (1999; Zbl 0933.11042)].

##### MSC:
 11M41 Other Dirichlet series and zeta functions 11B68 Bernoulli and Euler numbers and polynomials 05A30 $$q$$-calculus and related topics
##### Citations:
Zbl 0931.11031; Zbl 0675.12010; Zbl 0933.11042
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