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dc.contributor.authorLovejoy, Jeremy
dc.contributor.authorOsburn, Robert
dc.date.accessioned2017-10-25T08:11:07Z
dc.date.available2017-10-25T08:11:07Z
dc.date.issued2017-10-20
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1317
dc.descriptionResearch in Pairs 2016en_US
dc.description.abstractUsing a result of Takata, we prove a formula for the colored Jones polynomial of the double twist knots $K_{(-m,-p)}$ and $K_{(-m,p)}$ where $m$ and $p$ are positive integers. In the $(-m,-p)$ case, this leads to new families of $q$-hypergeometric series generalizing the Kontsevich-Zagier series. Comparing with the cyclotomic expansion of the colored Jones polynomials of $K_{(m,p)}$ gives a generalization of a duality at roots of unity between the Kontsevich-Zagier function and the generating function for strongly unimodal sequences.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2017,29
dc.subjectDouble Twist Knotsen_US
dc.subjectColored Jones Polynomialen_US
dc.subjectDualityen_US
dc.titleThe Colored Jones Polynomial and Kontsevich-Zagier Series for Double Twist Knotsen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2017-29
local.scientificprogramResearch in Pairs 2016en_US
local.series.idOWP-2017-29
local.subject.msc57
dc.identifier.urnurn:nbn:de:101:1-201801093146
dc.identifier.ppn1658648374


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