ON ANALYTIC PROPERTIES AND CHARACTER ANALOGS OF HARDY SUMS

Simsek Y.

TAIWANESE JOURNAL OF MATHEMATICS, cilt.13, sa.1, ss.253-268, 2009 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 1
  • Basım Tarihi: 2009
  • Doi Numarası: 10.11650/twjm/1500405282
  • Dergi Adı: TAIWANESE JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.253-268
  • Anahtar Kelimeler: ((x))-function, Dedekind sum, Hardy sums, Farey fraction, Dirichlet character and L-function, Generalized Bernoulli numbers, THETA-FUNCTIONS, SERIES, EISENSTEIN
  • Akdeniz Üniversitesi Adresli: Evet

Özet

The aim of this paper is to define Y(h, k) sum which is related to the Hardy's sums 85 (h, k). On the semi-group G, matrix operation of this sum is defined. Substituting mediants of Farey fractions into the matrix operation, Y(h, k) sum is generalized. By using contour integration, the reciprocity theorem of the Y(h, k) sum is proved. Moreover, by using L(1, chi) function and Gauss sums, generalized character analogs of the Hardy sums are found.