A note on the analogs of p-adic L-functions and sums of powers

T. Kim, C.S. Ryoo, H. K. Pak and S.-H. Rim
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 7, 2001, Number 3, Pages 78—86
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Authors and affiliations

T. Kim,
Institute of Science Education,
Kongju National University, Kongju 314-701, S. Korea

C.S. Ryoo
Deaprtment of Mathematics ,
Kyungpook University, Taegu 702-701, S. Korea

H. K. Pak
Department of Mathematics Kyungsan university,
Kyungsan, S. Korea

S.-H. Rim
Department of mathematics Education Kyungpook Unversity,
Taegu 702-701, S. Korea


The purpose of this paper is to give an explicit p-adic expansion of \sum_{j=1}^{*np} \frac{q^j}{j^r} such that the coefficients of the expansion are the values of an analogue of p-adic L-function associated with Euler numbers.


  • p-adic L-function
  • Bernoulli numbers
  • Dirichlet’s series

AMS Classification

  • 11B68
  • 11S80


  1. G.E. Andrews, q-analogs of the binomial coefficient congruences of Babbage, Wolstenholme and Glaisher, Discrete Math. 204 (1999), 15-25.
  2. T. Kim, On a q-analogue of p-adic log gamma functions and related integrals, J. Number Theory 78 (1999), 320-329.
  3.  ______, A note on p-adic Carlitz’s q-Bernoulli numbers, Bulletin Austral. Math.. 62 (2000), 227-234.
  4.  ______, Sums products of q-Bemoulli numbers, Arch. Math. 76 no. 3 (2001), 190-195.
  5.  ______, On p-adic qL-functions and sums of powers, Discrete Math. (2001).
  6.  ______, A note on p-adic q-Dedekind sums, Comptes Rendus de l’Academie Bulgare des Sciences 54 no. 10 (2001), 37-42.
  7. ______, Remark on p-adic q-Bernoulli numbers, Adv. Stud. Contemp. Math. (Kudeok Publ.) 1 (1999), 127-136.
  8.  ______, Some q-Bemoulli numbers of higher order associated with the p-adic q-integrals, Indian J. Pure and Appl. Math. 32 no. 10 (2001), 1565-1570.
  9.  ______, An analogue of Bernoulli numbers and their congruences, Rep. Fac. Sci. Engrg. Saga Univ. Math. 22 (1994), 7-13.
  10.  L.C. Jang, T. Kim, D-H. Lee, D-W. Park, An application of polylogarithms in the analogs of Genocchi numbers, Notes on Number Theory and Discrete Mathematics 7 no. 3 (2001), 65-69.
  11.  L. C. Washington, p-adic L-functions and sums of powers, J. Number Theory 69 (1998), 50-61.

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Cite this paper

Kim, T. , Ryoo, C.S., Pak, H. K. & Rim, S.-H. (2001). A note on the analogs of p-adic L-functions and sums of powers. Notes on Number Theory and Discrete Mathematics, 7(3), 78-86.

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