DC Field Value Language
dc.contributor.author이정연-
dc.date.accessioned2017-08-29T05:34:38Z-
dc.date.available2017-08-29T05:34:38Z-
dc.date.issued2017-
dc.identifier.issn0022-314X-
dc.identifier.otherOAK-19212-
dc.identifier.urihttp://dspace.ewha.ac.kr/handle/2015.oak/232686-
dc.description.abstractIn [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&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.-
dc.languageEnglish-
dc.subjectGeneralized Dedekind sums-
dc.subjectMeyer&apos;s formula-
dc.subjectPartial zeta function-
dc.subjectSiegel&apos;s formula-
dc.titleHigher Hickerson formula-
dc.typeArticle-
dc.relation.volume170-
dc.relation.indexSCI-
dc.relation.indexSCIE-
dc.relation.indexSCOPUS-
dc.relation.startpage191-
dc.relation.lastpage210-
dc.relation.journaltitleJournal of Number Theory-
dc.identifier.doi10.1016/j.jnt.2016.06.003-
dc.identifier.wosidWOS:000384394100013-
dc.identifier.scopusid2-s2.0-84981194106-
dc.contributor.scopusid이정연(23667995100;57188831777)-
dc.date.modifydate20180901081003-
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