Degenerate and character Dedekind sums

Cenkci M., Can M., Kurt V.

JOURNAL OF NUMBER THEORY, cilt.124, sa.2, ss.346-363, 2007 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 124 Sayı: 2
  • Basım Tarihi: 2007
  • Doi Numarası: 10.1016/j.jnt.2006.09.006
  • Dergi Adı: JOURNAL OF NUMBER THEORY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.346-363
  • Anahtar Kelimeler: Dedekind sums, Bernoulli polynomials, FORMULAS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, we study on two subjects. We first construct degenerate analogues of Dedekind sums in the sense of Apostol, Carlitz and Takacs, and prove the corresponding reciprocity formulas. Secondly, we define generalized Dedekind character sums, which are explicit extensions of Berndt's definition, and prove the reciprocity laws. From the derived reciprocity laws, we obtain Berndt's reciprocity laws as special cases. (C) 2006 Elsevier Inc. All rights reserved.