Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-07-01T03:03:39.046Z Has data issue: false hasContentIssue false
  • English
  • Français

NOTE ON q-DEDEKIND-TYPE SUMS RELATED TO q-EULER POLYNOMIALS

Published online by Cambridge University Press:  09 December 2011

TAEKYUN KIM
TAEKYUN KIM*
Affiliation:
Division of General Education-Mathematics, Kwangwoon University, Seoul 139-701, S. Korea e-mail: tkkim@kw.ac.kr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Recently, q-Dedekind-type sums related to q-zeta function and basic L-series are studied by Simsek in [13] (Y. Simsek, q-Dedekind type sums related to q-zeta function and basic L-series, J. Math. Anal. Appl. 318 (2006), 333–351) and Dedekind-type sums related to Euler numbers and polynomials are introduced in the previous paper [11] (T. Kim, Note on Dedekind type DC sums, Adv. Stud. Contem. Math. 18 (2009), 249–260). It is the purpose of this paper to construct a p-adic continuous function for an odd prime to contain a p-adic q-analogue of the higher order Dedekind the type sums related to q-Euler polynomials and numbers by using an invariant p-adic q-integrals.

Keywords

11B6811S80
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 1 , January 2012 , pp. 121 - 125
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

REFERENCES

1.Apostol, T. M., Generalized Dedekind sums and transformation formulae of certain Lambert series, Duke Math. J. 17 (1950), 147–157.CrossRefGoogle Scholar
2.Berndt, B. C., Generalized Dedekind eta functions and generalized Dedekind sums, Trans. Am. Math. Soc. 178 (1973), 495–508.CrossRefGoogle Scholar
3.Berndt, B. C., Dedekind sums and paper of G. H. Hardy, J. Lond. Math. Soc. 13 (1976), 129–136.CrossRefGoogle Scholar
4.Can, M., Cenkci, M., Kurt, V. and Simsek, Y., Twisted Dedekind type sums associated with Barnes' type multiple Frobenius-Euler l-functions, Adv. Stud. Contemp. Math. 18 (2009), 135–160.Google Scholar
5.Cenkci, M., Can, M. and Kurt, V., p-adic interpolation functions and Kummer-type congruences for q-twisted Euler numbers, Adv. Stud. Contemp. Math. 9 (2004), 203–216.Google Scholar
6.Kim, T., A note on p-adic q-Dedekind sums, C. R. Acad. Bulgare Sci. 54 (2001), 37–42.Google Scholar
7.Kim, T., q-Volkenborn integration, Russ. J. Math. Phys. 9 (2002), 288–299.Google Scholar
8.Kim, T., q-Euler numbers and polynomials associated with p-adic q-integrals, J. Nonlinear Math. Phys. 14 (2007), 15–27.CrossRefGoogle Scholar
9.Kim, T., The modified q-Euler numbers and polynomials, Adv. Stud. Contemp. Math. 16 (2008), 161–170.Google Scholar
10.Kim, T., On p-adic interpolating function for q-Euler numbers and its derivatives, J. Math. Anal. Appl. 339 (2008), 598–608.CrossRefGoogle Scholar
11.Kim, T., Note on Dedekind type DC sums, Adv. Stud. Contemp. Math. 18 (2009), 249–260.Google Scholar
12.Simsek, Y., Generalized Dedekind sums associated with the Abel sums and the Eisenstein and Lambert series, Adv. Stud. Contemp. Math. 9 (2004), 195–202.Google Scholar
13.Simsek, Y., q-Dedekind type sums related to q-zeta function and basic L-series, J. Math. Anal. Appl. 318 (2006), 333–351.CrossRefGoogle Scholar
14.Simsek, Y., Special functions related to Dedekind-type DC-sums and their applications, Russ. J. Math. Phys. 17 (2010), 495–508.CrossRefGoogle Scholar