TY - JOUR
AU - 이정연
DA - 2017
UR - http://dspace.ewha.ac.kr/handle/2015.oak/232686
AB - In [11], 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's original one and reduces to Hickerson'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'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'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.
LA - English
PB - Academic Press Inc.
KW - Generalized Dedekind sums
KW - Meyer's formula
KW - Partial zeta function
KW - Real quadratic fields
KW - Siegel's formula
TI - Higher Hickerson formula
VL - 170
DO - 10.1016/j.jnt.2016.06.003
ER -