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On the analogs of Bernoulli and Euler numbers, related identities and zeta and L-functions

김태균|임석훈|김대열|Yilmaz Simsek
대한수학회 (The Korean Mathematical Society)|2008.03|대한수학회지 (Journal of the KMS)|제45권 제2호|pp. 435-453

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참고문헌

키워드

Bernoulli numbers and polynomialszeta functions.
주제분류수학

초록

In this paper, by using q-deformed bosonic p-adic integral, we give λ-Bernoulli numbers and polynomials, we prove Witt’s type formula of λ-Bernoulli polynomials and Gauss multiplicative formula for λ-Bernoulli polynomials. By using derivative operator to the generating functions of λ-Bernoulli polynomials and generalized λ-Bernoulli numbers, we give Hurwitz type λ-zeta functions and Dirichlet’s type λ-L-functions; which are interpolated λ-Bernoulli polynomials and generalized λ-Bernoulli numbers, respectively. We give generating function of λ-Bernoulli numbers with order r. By using Mellin transforms to their function, we prove relations between multiply zeta function and λ-Bernoulli polynomials and ordinary Bernoulli numbers of order r and λ-Bernoulli numbers, respectively. We also study on λ-Bernoulli numbers and polynomials in the space of locally constant. Moreover, we define λ-partial zeta function and interpolation function.

Abstract

In this paper, by using q-deformed bosonic p-adic integral, we give λ-Bernoulli numbers and polynomials, we prove Witt’s type formula of λ-Bernoulli polynomials and Gauss multiplicative formula for λ-Bernoulli polynomials. By using derivative operator to the generating functions of λ-Bernoulli polynomials and generalized λ-Bernoulli numbers, we give Hurwitz type λ-zeta functions and Dirichlet’s type λ-L-functions; which are interpolated λ-Bernoulli polynomials and generalized λ-Bernoulli numbers, respectively. We give generating function of λ-Bernoulli numbers with order r. By using Mellin transforms to their function, we prove relations between multiply zeta function and λ-Bernoulli polynomials and ordinary Bernoulli numbers of order r and λ-Bernoulli numbers, respectively. We also study on λ-Bernoulli numbers and polynomials in the space of locally constant. Moreover, we define λ-partial zeta function and interpolation function.

참고문헌 (29)

  1. E. W. Barnes, "On the theory of the multiple gamma functions", Transactions of the Cambridge philosophical Society, 19, pp.374~425 (1994)
  2. K. C. Garret, "A combinatorial proof of the sum of q-cubes", Electronic Journal of Combinatorics, 11(1), pp.9~ (2004)
  3. K. Iwasawa, "Lectures on p-adic L-function, Annals of Mathematics Studies, No. 74" (1972), Princeton University Press
  4. L. C. Jang, "Non-Archimedean integration associated with q-Bernoulli numbers", Proc. Jangjeon Math. Soc., 통권 : 5, pp.125~129 (2002)
  5. T. Kim, "An analogue of Bernoulli numbers and their congruences", Reports of the Faculty of Science and Engineering. Saga University. Mathematics, 22(2), pp.21~26 (1994)
  6. T. Kim, "On a q-analogue of the p-adic log gamma functions and related integrals", Journal of Number Theory, 76(2), pp.320~329 (1999)
  7. T. Kim, "q-Volkenborn integration", Russian Journal of Mathematical Physics, 9(3), pp.288~299 (2002)
  8. T. Kim, "An invariant p-adic integral associated with Daehee numbers", Integral Transforms and Special Functions, 13(1), pp.65~69 (2002)
  9. T. Kim, "On Euler-Barnes multiple zeta functions", Russian Journal of Mathematical Physics, 10(3), pp.261~267 (2003)
  10. T. Kim, "A note on multiple zeta functions", JP Journal of Algebra Number Theory and Applications, 3(3), pp.471~476 (2003)
  11. T. Kim, "Non-archimedean q-integrals associated with multiple Changhee q-Bernoulli Polynomials", Russian Journal of Mathematical Physics, 10(1), pp.91~98 (2003)
  12. T. Kim, "Remark on the multiple Bernoulli numbers", Proceedings of the Jangjeon Mathematical Society, 통권 : 6, pp.185~192 (2003)
  13. T. Kim, "Sums of powers of consecutive q-integers", Advanced Studies in Contemporary Mathematics (Kyungshang), 9(1), pp.15~18 (2004)
  14. T. Kim, "Analytic continuation of multiple q-zeta functions and their values at negative integers", Russian Journal of Mathematical Physics, 11(1), pp.71~76 (2004)
  15. T. Kim, "A note on multiple Dirichlet’s q-L-function", Advanced Studies in Contemporary Mathematics (Kyungshang), 11(1), pp.57~60 (2005)
  16. T. Kim, "Power series and asymptotic series associated with the q-analog of the twovariable p-adic L-function", Russian Journal of Mathematical Physics, 12(2), pp.186196~ (2005)
  17. T. Kim, "Multiple p-adic L-function", Russian Journal of Mathematical Physics, 13, pp.151~157 (2006)
  18. T. Kim, "A new approach to p-adic q-L-functions", Advanced Studies in Contemporary Mathematics (Kyungshang), 12(1), pp.61~72 (2006)
  19. T. Kim, "On the analogs of Euler numbers and polynomials associated with p-adic q-integral on Zp at q = ¡1", Journal of Mathematical Analysis and Applications (2006)
  20. T. Kim, "A note on q-Bernoulli numbers and polynomials", Journal of Nonlinear Mathematical Physics, 13, pp.315~320 (2006)
  21. T. Kim, "On the twisted q-zeta functions and q-Bernoulli polynomials", Far East Journal of Applied Mathematics, 13(1), pp.13~21 (2003)
  22. J. Satho, "q-analogue of Riemann’s ³-function and q-Euler numbers", Journal of Number Theory, 31(3), pp.346~362 (1989)
  23. M. Schlosser, "q-analogues of the sums of consecutive integers, squares, cubes, quarts and quints, Electron", Journal of Combinatorial Theory, 11(1), pp.71~ (2004)
  24. K. Shiratani, "On a p-adic interpolation function for the Euler numbers and its derivatives", Memoirs of the Faculty of Science Kyushu University Series A, 39(1), pp.113~125 (1985)
  25. Y. Simsek, "Theorems on twisted L-functions and twisted Bernoulli numbers", Advanced Studies in Contemporary Mathematics (Kyungshang), 11(2), pp.205~218 (2005)
  26. Y. Simsek, "Twisted (h; q)-Bernoulli numbers and polynomials related to (h; q)-zeta function and L-function", Journal of Mathematical Analysis and Applications, 324, pp.790~804 (2006)
  27. Y. Simsek, "A note on the sums of powes of consecutive q-integers", Journal of Applied Functional Differential Equation, 1, pp.63~70 (2006)
  28. Y. Simsek, "Transformation of four Titchmarsh-type infinite integrals and generalized Dedekind sums associated with Lambert series", Advanced Studies in Contemporary Mathematics (Kyungshang), 9(2), pp.195~202 (2004)
  29. H. M. Srivastava, "q-Bernoulli multiple q-zeta functions and basic L-series", Russian Journal of Mathematical Physics, 12(2), pp.241~268 (2005)

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