A note on the modified q-Dedekind sums

Serkan Araci, Erdoğan Şen and Mehmet Acikgoz
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 19, 2013, Number 3, Pages 60—65
Download full paper: PDF, 184 Kb

Details

Authors and affiliations

Serkan Araci
Department of Mathematics, Faculty of Science and Arts, University of Gaziantep
27310 Gaziantep, Turkey

Erdoğan Şen
Department of Mathematics, Faculty of Science and Letters, Namık Kemal University
59030 Tekirdağ, Turkey

Mehmet Acikgoz
Department of Mathematics, Faculty of Science and Arts, University of Gaziantep
27310 Gaziantep, Turkey

Abstract

In the present paper, the fundamental aim is to consider a p-adic continuous function for an odd prime to inside a p-adic q-analogue of the higher order Extended Dedekind-type sums related to q-Genocchi polynomials with weight α by using fermionic p-adic invariant q-integral on ℤp.

Keywords

  • Dedekind Sums
  • q-Dedekind-type Sums
  • p-adic q-integral
    q-Genocchi polynomials with weight α

AMS Classification

  • 11S80
  • 11B68

References

  1. Araci, S., D. Erdal, J. J. Seo. A study on the fermionic p-adic q-integral representation on ℤp associated with weighted q-Bernstein and q-Genocchi polynomials, Abstract and Applied Analysis, Vol. 2011, Article ID 649248, 10 pages.
  2. Araci, S., M. Acikgoz, J. J. Seo. Explicit formulas involving q-Euler numbers and polynomials, Abstract and Applied Analysis, Vol. 2012, Article ID 298531, 11 pages.
  3. Araci, S., J. J. Seo, D. Erdal. New construction weighted (h; q)-Genocchi numbers and polynomials related to Zeta-type functions, Discrete Dynamics in Nature and Society, Vol. 2011, 2011, Article ID 487490, 7 pages.
  4. Araci, S., M. Acikgoz, K. H. Park, H. Jolany. On the unification of two families of multiple twisted type polynomials by using p-adic q-integral on ℤp at q = −1, accepted in Bulletin of the Malaysian Mathematical Sciences and Society.
  5. Araci, S., M. Acikgoz, H. Jolany, J. J. Seo. A unified generating function of the q-Genocchi polynomials with their interpolation functions, Proc. Jangjeon Math. Soc. Vol. 15, 2012, No. 2, 227–233.
  6. Araci, S., M. Acikgoz, K. H. Park. A note on the q -analogue of Kim’s p-adic log gamma type functions associated with q-extension of Genocchi and Euler numbers with weight α, accepted in Bulletin of the Korean Mathematical Society.
  7. Araci, S., M. Acikgoz, J. J. Seo. A study on the weighted q-Genocchi numbers and polynomials with their interpolation function, Honam Mathematical J., Vol. 34, 2012, No. 1, 11–18.
  8. Acikgoz, M., S. Araci, I. N. Cangul. A note on the modified q-Bernstein polynomials for functions of several variables and their reflections on q-Volkenborn integration, Applied Mathematics and Computation, Vol. 218, 2011, No. 3, 707–712.
  9. Kim, T. A note on p-adic q-Dedekind sums, C. R. Acad. Bulgare Sci., Vol. 54, 2001, 37–42.
  10. Kim, T. Note on q-Dedekind-type sums related to q-Euler polynomials, Glasgow Math. J., Vol. 54, 2012, 121–125.
  11. Kim, T. Note on Dedekind type DC sums, Adv. Stud. Contemp. Math, Vol. 18, 2009, 249– 260.
  12. Kim, T. The modified q-Euler numbers and polynomials, Adv. Stud. Contemp. Math., Vol. 16, 2008, 161–170.
  13. Kim, T. q-Volkenborn integration, Russ. J. Math. Phys., Vol. 9, 2002, 288–299.
  14. Kim, T. On p-adic interpolating function for q-Euler numbers and its derivatives, J. Math. Anal. Appl., Vol. 339, 2008, 598–608.
  15. Kim, T. On a q-analogue of the p-adic log gamma functions and related integrals. J. Number Theory, Vol. 76, 1999, 320–329.
  16. Kim, T. On the weighted q-Bernoulli numbers and polynomials, Advanced Studies in Contemporary Mathematics, Vol. 21, 2011, No. 2, 207–215.
  17. Kim, T., J. Choi, On the q-Euler Numbers and Polynomials with Weight 0, Abstract and Applied Analysis, Vol. 2012, Article ID 795304, 7 pages.
  18. Simsek, Y. q-Dedekind type sums related to q-zeta function and basic L-series, J. Math. Anal. Appl., Vol. 318, 2006, 333–351.
  19. Acikgoz, M., Y. Simsek, On multiple interpolation function of the Nörlund-type q-Euler polynomials, Abst. Appl. Anal., Vol. 2009, 2009, Article ID 382574, 14 pages.

Related papers

Cite this paper

APA

Araci, S., Şen, E., & Acikgoz, M. (2013). A note on the modified q-Dedekind sums. Notes on Number Theory and Discrete Mathematics, 19(3), 60-65.

Chicago

Araci, Serkan, Erdoğan Şen and Mehmet Acikgoz. “A Note on the Modified q-Dedekind Sums.” Notes on Number Theory and Discrete Mathematics 19, no. 3 (2013): 60-65.

MLA

Araci, Serkan, Erdoğan Şen and Mehmet Acikgoz. “A Note on the Modified q-Dedekind Sums.” Notes on Number Theory and Discrete Mathematics 19.3 (2013): 60-65. Print.

Comments are closed.