In
[11], Hickerson made an explicit formula for Dedekind sums
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301548&_mathId=si1.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=a793f7facdb680f1d93c110e62574a92" title="Click to view the MathML source">s(p,q)class="mathContainer hidden">class="mathCode"> in terms of the continued fraction of
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301548&_mathId=si2.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=c754417fa40160ef3561c82ad5e61478" title="Click to view the MathML source">p/qclass="mathContainer hidden">class="mathCode">. We develop analogous formula for generalized Dedekind sums
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301548&_mathId=si3.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=50921a92e992d9bcb46d77112310dc01" title="Click to view the MathML source">si,j(p,q)class="mathContainer hidden">class="mathCode"> defined in association with the
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301548&_mathId=si4.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=6d8bba80a3ff6f6fa5cbf0fd6f7131e9" title="Click to view the MathML source">xiyjclass="mathContainer hidden">class="mathCode">-coefficient of the Todd power series of the lattice cone in
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301548&_mathId=si5.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=a6e0cd47c5e9badb8a166515fc840d6b" title="Click to view the MathML source">R2class="mathContainer hidden">class="mathCode"> generated by
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301548&_mathId=si6.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=92f11dee46d081ca88d5b5d14cd7c151" title="Click to view the MathML source">(1,0)class="mathContainer hidden">class="mathCode"> and
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301548&_mathId=si7.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=3481483978028da6fd62d31f9d298748" title="Click to view the MathML source">(p,q)class="mathContainer hidden">class="mathCode">. The formula generalizes Hickerson's original one and reduces to Hickerson's for
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301548&_mathId=si8.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=956405bad31eb5d3a361ec5075979e01" title="Click to view the MathML source">i=j=1class="mathContainer hidden">class="mathCode">. In the formula, generalized Dedekind sums are divided into two parts: the integral
class="mathmlsrc">title="View 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">class="imgLazyJSB inlineImage" 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">class="mathContainer hidden">class="mathCode"> and the fractional
class="mathmlsrc">title="View 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">class="imgLazyJSB inlineImage" 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">class="mathContainer hidden">class="mathCode">. We apply the formula to Siegel's formula for partial zeta values at a negative integer and obtain a new expression which involves only
class="mathmlsrc">title="View 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">class="imgLazyJSB inlineImage" 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">class="mathContainer hidden">class="mathCode"> 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
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301548&_mathId=si11.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=689ff79aa1b80b4bb5d1d0ad78b952b6" title="Click to view the MathML source">s=−1class="mathContainer hidden">class="mathCode"> and −2 in more explicit form. Finally, we present another application on the equidistribution property of the fractional parts of the graph
class="mathmlsrc">title="View 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">class="imgLazyJSB inlineImage" 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">class="mathContainer hidden">class="mathCode"> for a certain integer
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301548&_mathId=si13.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=285c25c2919bc817ce00b24b2077146a" title="Click to view the MathML source">Ri+jclass="mathContainer hidden">class="mathCode"> depending on
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301548&_mathId=si14.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=feebb1991c9eb9545515f1bc4b33537f" title="Click to view the MathML source">i+jclass="mathContainer hidden">class="mathCode">.