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On a \(q\)-analogue of the \(p\)-adic log gamma functions and related integrals. (English) Zbl 0941.11048

The author proposes a definition of a \(q\)-analogue of the \(p\)-adic Haar distribution. The resulting Volkenborn-type integral leads, in particular, to an integral representation of \(q\)-Bernoulli numbers. In turn, the latter is used for obtaining new identities for \(q\)-Bernoulli numbers, \(q\)-Bernoulli polynomials, and for a \(q\)-analogue of the Diamond log gamma function.

MSC:

11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
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[1] Carlitz, L., q, Duke math. J., 15, 987-1000, (1948) · Zbl 0032.00304
[2] Diamond, J., Thepp, Trans. amer. math. soc., 233, 321-337, (1977) · Zbl 0382.12008
[3] Ikeda, K.; Kim, T.; Shiratani, K., Onp, Mem. fac. sci. kyushu univ., 36, 301-309, (1992)
[4] Kim, T., An analogue of Bernoulli numbers and their congruences, Rep. fac. sci. engrg. saga univ. math., 22, 7-13, (1994)
[5] Koblitz, N., qp, Trans. amer. math. soc., 260, 449-457, (1980)
[6] Koblitz, N., A new proof of certain formulas forpL, Duke math. J., 46, 445-468, (1979)
[7] Koblitz, N., On Carlitz’sq, J. number theory, 14, 332-339, (1982) · Zbl 0501.12020
[8] Satoh, J., qζq, J. number theory, 31, 346-362, (1989) · Zbl 0675.12010
[9] Shiratani, K.; Yamamoto, S., On ap, Mem. fac. sci. kyushu univ., 39, 113-125, (1985) · Zbl 0574.12017
[10] Shiratani, K., An application ofp, Kyungpook math. J., 34, 239-246, (1994) · Zbl 0829.11064
[11] Woodcock, C.F., A two variable Riemann zeta function, J. number theory, 27, 212-221, (1987) · Zbl 0623.10028
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