In
[11], Hickerson made an explicit formula for Dedekind sums
s(p,q) in terms of the continued fraction of
a40160ef3561c82ad5e61478" title="Click to view the MathML source">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
a46641bb">
mage" height="21" width="55" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022314X16301548-si9.gif"> and the fractional
mage" height="21" width="55" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022314X16301548-si10.gif">. We apply the formula to Siegel's formula for partial zeta values at a negative integer and obtain a new expression which involves only
a46641bb">
mage" height="21" width="55" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022314X16301548-si9.gif"> 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
a4fa5535f840f">
mage" height="29" width="167" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022314X16301548-si12.gif"> for a certain integer
Ri+j depending on
i+j.