Journal of the Korean Mathematical Society (대한수학회지)

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ON A q-ANALOGUE OF THE p-ADIC GENERALIZED TWISTED L-FUNCTIONS AND p-ADIC q-INTEGRALS

  • Lee, Chae-Jang (Department of Mathematics and Computater Science KonKuk University)
  • Published : 2007.01.31
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Abstract

The purpose of this paper is to define generalized twisted q-Bernoulli numbers by using p-adic q-integrals. Furthermore, we construct a q-analogue of the p-adic generalized twisted L-functions which interpolate generalized twisted q-Bernoulli numbers. This is the generalization of Kim's h-extension of p-adic q-L-function which was constructed in [5] and is a partial answer for the open question which was remained in [3].

Keywords

References

  1. G. E. Andrews, Number Theory, W. B. Saunder Company, Philandelphia, London- Toronto, 1971
  2. G. Bachmann, Introduction to p-adic numbers and valuation theory, Academic Press, New York-London, 1964
  3. T. Kim, L. C. Jang, S. G. Rim, and H. K. Pak, On the twisted q-zeta functions and q-Bernoulli polynomials, Far East J. Appl. Math. 13 (2003), no. 1, 13-21
  4. T. Kim and S. H. Rim, Generalized Carlitz's q-Bernoulli numbers in the p-adic number field, Adv. Stud. Contemp. Math. (Pusan) 2 (2000), 9-19
  5. T. Kim, q-Volkenborn integration, Russ. J. Math. Phys. 9 (2002), no. 3, 288-299
  6. T. Kim, On Euler-Barnes multiple zeta functions, Russ. J. Math. Phys. 10 (2003), no. 3, 261-267
  7. 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 https://doi.org/10.1006/jnth.1999.2373
  8. T. Kim, p-adic q-integrals associated with Changhee-Barnes' q-Bernoulli polynomials, Integral Transforms Spec. Funct. 15 (2004), no. 5, 415-420 https://doi.org/10.1080/10652460410001672960
  9. T. Kim, Non-Archimedean q-integrals associated with multuple Changhee q-Bernoulli polynomials, Russ. J. Math. Phys. 10 (2003), no. 1, 91-98
  10. T. Kim, Analytic continuation of multiple q-zeta functions and their values, Russ. J. Math. Phys. 11 (2004), no. 1, 71-76
  11. T. Kim, q-Riemann zeta functions, Int. J. Math. Math. Sci. 12 (2004), no. 9-12, 599-605
  12. T. Kim, On p-adic q - L-functions and sums of powers, Discrete Math. 252 (2002), no. 1-3, 179-187 https://doi.org/10.1016/S0012-365X(01)00293-X
  13. T. Kim, On explicit formulas of p-adic q - L-functions, Kyushu J. Math. 48 (1994), no. 1, 73-86 https://doi.org/10.2206/kyushujm.48.73
  14. T. Kim, Sums of powers of consecutive q-integers, Adv. Stud. Contemp. Math. (Kyung-shang) 9 (2004), no. 1, 15-18
  15. N. Koblitz, A new proof of certain formulas for p-adic L-functions, Duke Math. J. 46 (1979), no. 2, 455-468 https://doi.org/10.1215/S0012-7094-79-04621-0
  16. N. Koblitz, p-adic numbers, p-adic analysis and Zeta functions, Graduate Texts in Math-ematics, Vol. 58. Springer-Verlag, New York-Heidelberg, 1977
  17. N. Koblitz, On Carlitz's q-Bernoulli numbers, J. Number Theory 14 (1982), no. 3, 332-339 https://doi.org/10.1016/0022-314X(82)90068-3
  18. N. Koblitz, p-adic numbers and their functions, Springer-Verlag, GTM 58, 1984
  19. A. M. Robert, A course in p-adic analysis, Graduate Texts in Mathematics, 198. Springer-Verlag, New York, 2000
  20. W. H. Schikhof, Ultrametric Calculus, Cambridge Studies in Advanced Mathematics, 4. Cambridge University Press, Cambridge, 1984
  21. K. Shiratani and S. Yamamoto, On a p-adic interpolating function for the Euler number and its derivative, Mem. Fac. Sci. Kyushu Univ. Ser. A 39 (1985), no. 1, 113-125
  22. Y. Simsek, On p-adic twisted q - L-functions related to generalized twisted Bernoulli numbers, Russian J. Math. Phys. 13 (2006), no. 3, 340-348 https://doi.org/10.1134/S1061920806030095
  23. Y. Simsek, Twisted (h,q)-Bernoulli numbers and polynomials related to twisted (h; q)-zeta function and L-function, J. Math. Anal. Appl. 324 (2006), no. 2, 790-804 https://doi.org/10.1016/j.jmaa.2005.12.057
  24. Y. Simsek, Theorems on twisted L-functions and twisted Bernoulli numbers, Adv. Stud. Contemp. Math. 11 (2005), no. 2, 205-218
  25. A. C. M. van Rooji, Non-Archimedean Functional Analysis, Monographs and Textbooks in Pure and Applied Math., 51. Marcel Dekker, Inc., New York, 1978
  26. L. C. Washington, Introduction to Cyclotomic fields, Graduate Texts in Mathematics, 83. Springer-Verlag, New York, 1997

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