Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

SOME REMARKS ON A q-ANALOGUE OF BERNOULLI NUMBERS

  • Published : 2002.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

Using the p-adic q-integral due to T. Kim[4], we define a number B＊$_{n}$(q) and a polynomial B＊$_{n}$(q) which are p-adic q-analogue of the ordinary Bernoulli number and Bernoulli polynomial, respectively. We investigate some properties of these. Also, we give slightly different construction of Tsumura＇s p-adic function $\ell$$_{p}$(u, s, $\chi$) [14] using the p-adic q-integral in [4].n [4].

Keywords

References

  1. Duke Math. J. v.15 q-Bernoulli numbers and polynomials L. Carlitz https://doi.org/10.1215/S0012-7094-48-01588-9
  2. Rep. Fac. Sci. Engrg. Saga Univ. Math. v.22 An analogue of Bernoulli numbers and their congruences T. Kim
  3. Kyushu J. Math. v.48 On explicit formulas of p-adic q-L-functions https://doi.org/10.2206/kyushujm.48.73
  4. J. Number Theory v.76 On a q-analogue of the p-adic log gamma functions and related integral https://doi.org/10.1006/jnth.1999.2373
  5. Comptes Rendus De l’Academine Bulgare des Sciences A note on p-adic Dedekind sums
  6. Notes Number Theory Discrete Math. A note on the values of zeta
  7. Advanced Studies in Contemporary Math. v.1 Remark on p-adic q-Bernoulli numbers T. Kim;H. S. Kim
  8. Bull. Korean Math. Soc. v.33 A remark on p-adic q-Bernoulli measure H. S. Kim;P.-S. Lim;T. Kim
  9. J. Korean Math. Soc. v.37 On Bernoulli numbers M.-S. Kim;J.-W. Son
  10. Duke Math. J. v.46 A new proof of certain formulas for p-adic L-functions N. Koblitz https://doi.org/10.1215/S0012-7094-79-04621-0
  11. J. Number Theory v.14 On Carlitz’s q-Bernoulli numbers https://doi.org/10.1016/0022-314X(82)90068-3
  12. p-adic Numbers, p-adic Analysis and Zeta-Functions, 2nd
  13. J. Number Theory v.31 q-analogue of Riemann’s ³-function and q-Euler numbers J. Satoh https://doi.org/10.1016/0022-314X(89)90078-4
  14. Tokyo J. Math. v.10 On a p-adic interpolation of the generalized Euler numbers and its applications H. Tsumura https://doi.org/10.3836/tjm/1270134514
  15. J. Number Theory v.39 A note on q-analogues of the Dirichlet series and q-Bernoulli numbers https://doi.org/10.1016/0022-314X(91)90048-G
  16. Introduction to Cyclotomic Fields, 2nd L. Washington

Cited by

  1. q-Analogue of twisted l-series and q-twisted Euler numbers vol.110, pp.2, 2005, https://doi.org/10.1016/j.jnt.2004.07.003