TAIWANESE JOURNAL OF MATHEMATICS, vol.13, no.1, pp.253-268, 2009 (SCI-Expanded)
Article / Article
TAIWANESE JOURNAL OF MATHEMATICS
Science Citation Index Expanded (SCI-EXPANDED), Scopus
((x))-function, Dedekind sum, Hardy sums, Farey fraction, Dirichlet character and L-function, Generalized Bernoulli numbers, THETA-FUNCTIONS, SERIES, EISENSTEIN
Akdeniz University Affiliated:
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.