q-EXTENSIONS OF GENOCCHI NUMBERS

Title & Authors
q-EXTENSIONS OF GENOCCHI NUMBERS
CENKCI MEHMET; CAN MUMUN; KURT VELI;

Abstract
In this paper q-extensions of Genocchi numbers are defined and several properties of these numbers are presented. Properties of q-Genocchi numbers and polynomials are used to construct q-extensions of p-adic measures which yield to obtain p-adic interpolation functions for q-Genocchi numbers. As an application, general systems of congruences, including Kummer-type congruences for q-Genocchi numbers are proved.
Keywords
q-Genocchi numbers;p-adic measures;p-adic integral;Kummer congruences;
Language
English
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References
1.
L. Carlitz, q-Bernoulli numbers and polynomials, Duke Math. J. 15 (1948), 987-1000

2.
L. Carlitz, q-Bernoulli and Eulerian numbers, Trans. Amer. Math. Soc. 76 (1954), 332-350

3.
L. Carlitz, The Staudt-Clausen theorem, Math. Mag. 34 (1961), 131-146

4.
M. Cenkci, M. Can, and V. Kurt, p-adic interpolation functions and Kummer-type congruences for q-twisted and q-generalized twisted Euler numbers, Advan. Stud. Contem. Math. 9 (2004), no. 2, 203-216

5.
G. -N. Han and J. Zeng, On a sequence that generalizes the median Genocchi numbers, Ann. Sci. Math. Quebec 23 (1999), no. 1, 63-72

6.
G. -N. Han, A. Randrianarivony, and J. Zeng, Un autre q-analogue des nombres d'Euler, Seminaire Lotharingien de Combinatorie 42 Art. B42e, (1999), 22pp. (electronic)

7.
F. T. Howard, Applications of a recurrence formula for the Bernoulli numbers, J. Number Theory 52 (1995), no. 1, 157-172

8.
K. Iwasawa, Lectures on p-adic L-functions, Ann. of Math. Studies Vol: 74, Princeton Univ. Press, Princeton, N. J., 1972

9.
L. -C. Jang, T. Kim, D. -H. Lee, and D. -W. Park, An application of polylogarithms in the analogs of Genocchi numbers, Notes Number Theory Discrete Math. 7 (2001), no. 3, 65-69

10.
T. Kim, On explicit formulas of p-adic q-L-functions, Kyushu J. Math. 48 (1994), no. 1, 73-86

11.
T. Kim, On a q-analogue of the p-adic log gamma functions and related integrals, J. Number Theory 76 (1999), no. 2, 320-329

12.
T. Kim, q-Volkenborn integration, Russ. J. Math. Phys. 9 (2002), no. 3, 288-299

13.
T. Kim, On p-adic q-L-functions and sums of powers, Discrete Math. 252 (2002), no. 1-3, 179-187

14.
T. Kim, Non-Archimedean q-integrals associated with multiple Changhee q- Bernoulli polynomials, Russ. J. Math. Phys. 10 (2003), no. 1, 91-98

15.
T. Kim, On Euler-Barnes multiple zeta functions, Russ. J. Math. Phys. 10 (2003), no. 3, 261-267

16.
T. Kim, A note on q-Volkenborn integration,(English. English summary) Proc. Jangjeon Math. Soc. 8 (2005), no. 1, 13-17

17.
T. Kim, L. -C. Jang, and H. K. Pak, A note on q-Euler and Genocchi numbers, Proc. Japan Acad. Ser. A Math. Sci. 77 (2001), no. 8, 139-141

18.
T. Kim, Y. Simsek, and H. M. Srivastava, q-Bernoulli numbers and polynomials associated with multiple q-zeta functions and basic L-series, Russ. J. Math. Phys. 12 (2005), no. 2, 201-228

19.
N. Koblitz, On Carlitz's q-Bernoulli numbers, J. Number Theory 14 (1982), no. 3, 332-339

20.
J. Satoh, q-analogue of Riemann's $\zeta$-function and q-Euler numbers, J. Number Theory 31 (1989), no. 3, 346-362

21.
P. T. Young, Congruences for Bernoulli, Euler and Stirling numbers, J. Number Theory 78 (1999), no. 2, 204-227

22.
P. T. Young, On the behaviour of some two-variable p-adic L-functions, J. Number Theory 98 (2003), no. 1, 67-88