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dc.contributor.authorLovejoy, Jeremy
dc.contributor.authorOsburn, Robert
dc.date.accessioned2023-07-12T12:10:07Z
dc.date.available2023-07-12T12:10:07Z
dc.date.issued2023-07-12
dc.identifier.urihttp://publications.mfo.de/handle/mfo/4054
dc.description.abstractWe prove general fomulas for the deviations of two overpartition ranks from the average, namely \begin{equation*} \overline{D}(a, M) := \sum_{n \geq 0} \Bigl( \overline{N}(a, M, n) - \frac{\overline{p}(n)}{M} \Bigr) q^n \end{equation*} and \begin{equation*} \overline{D}_{2}(a,M) := \sum_{n \geq 0} \Bigl( \overline{N}_{2}(a, M, n) - \frac{\overline{p}(n)}{M} \Bigr) q^n \end{equation*} where $\overline{N}(a, M, n)$ denotes the number of overpartitions of $n$ with rank congruent to $a$ modulo $M$, $\overline{N}_{2}(a, M, n)$ is the number of overpartitions of $n$ with $M_2$-rank congruent to $a$ modulo $M$ and $\overline{p}(n)$ is the number of overpartitions of $n$. These formulas are in terms of Appell-Lerch series and sums of quotients of theta functions and can be used, among other things, to recover any of the numerous overpartition rank difference identities in the literature. We give examples for $M=3$ and $6$.en_US
dc.description.sponsorshipThe authors would like to thank the Mathematisches Forschungsinstitut Oberwolfach for their support as this work began during their stay from January 9-22, 2022 as part of the Research in Pairs program. The second author was partially funded by a SSHN 2022 grant from the Embassy of France in Ireland during his visit to the Université Paris Cité from December 4-17, 2022. Finally, the authors are grateful to the Max-Planck-Institut für Mathematik for their hospitality and support during their joint stay from May 1-31, 2023.
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2023-11
dc.subjectOverpartitionsen_US
dc.subjectRanken_US
dc.subjectM2-Ranken_US
dc.subjectAppell-Lerch seriesen_US
dc.titleRank Deviations for Overpartitionsen_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-2023-11
local.scientificprogramOWRF 2022en_US
local.series.idOWP-2023-11en_US
local.subject.msc11en_US
local.subject.msc05en_US
dc.identifier.urnurn:nbn:de:101:1-2024032009224643417989
dc.identifier.ppn1858138884


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