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dc.contributor.authorBelmont, Eva
dc.contributor.authorLee, Holden
dc.contributor.authorMusat, Alexandra
dc.contributor.authorTrebat-Leder, Sarah
dc.date.accessioned2017-04-07T16:55:37Z
dc.date.available2017-04-07T16:55:37Z
dc.date.issued2013-11
dc.date.submitted2011-07
dc.identifier.issn0026-9255
dc.identifier.issn1436-5081
dc.identifier.urihttp://hdl.handle.net/1721.1/107942
dc.description.abstractFolsom, Kent, and Ono used the theory of modular forms modulo ℓ to establish remarkable “self-similarity” properties of the partition function and give an overarching explanation of many partition congruences. We generalize their work to analyze powers p[subscript r] of the partition function as well as Andrews’s spt-function. By showing that certain generating functions reside in a small space made up of reductions of modular forms, we set up a general framework for congruences for p[subscript r] and spt on arithmetic progressions of the form ℓ[superscript m]n+δℓ modulo powers of ℓ. Our work gives a conceptual explanation of the exceptional congruences of p[subscript r] observed by Boylan, as well as striking congruences of spt modulo 5, 7, and 13 recently discovered by Andrews and Garvan.en_US
dc.publisherSpringer Viennaen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s00605-013-0586-yen_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceSpringer Viennaen_US
dc.titleℓ-Adic properties of partition functionsen_US
dc.typeArticleen_US
dc.identifier.citationBelmont, Eva, Holden Lee, Alexandra Musat, and Sarah Trebat-Leder. “ℓ-Adic properties of partition functions.” Monatshefte Für Mathematik 173, no. 1 (November 6, 2013): 1–34.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.mitauthorBelmont, Eva
dc.relation.journalMonatshefte für Mathematiken_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2016-05-23T12:08:48Z
dc.language.rfc3066en
dc.rights.holderSpringer-Verlag Wien
dspace.orderedauthorsBelmont, Eva; Lee, Holden; Musat, Alexandra; Trebat-Leder, Sarahen_US
dspace.embargo.termsNen
dc.identifier.orcidhttps://orcid.org/0000-0003-3312-6665
mit.licensePUBLISHER_POLICYen_US


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