이정연 2017-08-29T05:34:38Z 2017-08-29T05:34:38Z 2017 0022-314X OAK-19212 http://dspace.ewha.ac.kr/handle/2015.oak/232686 In , Hickerson made an explicit formula for Dedekind sums s(p,q) in terms of the continued fraction of p/q. We develop analogous formula for generalized Dedekind sums si,j(p,q) defined in association with the xiyj-coefficient of the Todd power series of the lattice cone in R2 generated by (1,0) and (p,q). The formula generalizes Hickerson&apos;s original one and reduces to Hickerson&apos;s for i=j=1. In the formula, generalized Dedekind sums are divided into two parts: the integral sij I(p,q) and the fractional sij R(p,q). We apply the formula to Siegel&apos;s formula for partial zeta values at a negative integer and obtain a new expression which involves only sij I(p,q) the integral part of generalized Dedekind sums. This formula directly generalizes Meyer&apos;s formula for the special value at 0. Using our formula, we present the table of the partial zeta value at s=−1 and −2 in more explicit form. Finally, we present another application on the equidistribution property of the fractional parts of the graph (pq,Ri+jqi+j−2sij(p,q)) for a certain integer Ri+j depending on i+j. © 2016 Elsevier Inc. English Academic Press Inc. Generalized Dedekind sums Meyer&apos;s formula Partial zeta function Real quadratic fields Siegel&apos;s formula Higher Hickerson formula Article 170 SCI SCIE SCOPUS 191 210 Journal of Number Theory 10.1016/j.jnt.2016.06.003 WOS:000384394100013 2-s2.0-84981194106 Lee J. Jun B. Chae H.-J. 이정연(23667995100;57188831777) 20180901081003