In
[11], Hickerson made an explicit formula for Dedekind sums
w the MathML source">s(p,q) in terms of the continued fraction of
w the MathML source">p/q. We develop analogous formula for generalized Dedekind sums
w the MathML source">si,j(p,q) defined in association
with the
w the MathML source">xiyj-coefficient of the Todd po
wer series of the lattice cone in
w the MathML source">R2 generated by
w the MathML source">(1,0) and
w the MathML source">(p,q). The formula generalizes Hickerson's original one and reduces to Hickerson's for
w the MathML source">i=j=1. In the formula, generalized Dedekind sums are divided into t
wo parts: the integral
w the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301548&_mathId=si9.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=099c6f0e102a6cedc9ffbf32a46641bb">
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
w the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301548&_mathId=si10.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=d90ac1223f8bb67d181b25c20727c386">
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 ne
w expression
which involves only
w the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301548&_mathId=si9.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=099c6f0e102a6cedc9ffbf32a46641bb">
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
w the MathML source">s=−1 and −2 in more explicit form. Finally,
we present another application on the equidistribution property of the fractional parts of the graph
w the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301548&_mathId=si12.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=02df000922d3a943c32a4fa5535f840f">
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
w the MathML source">Ri+j depending on
w the MathML source">i+j.