dc.contributor.author | Belmont, Eva | |
dc.contributor.author | Lee, Holden | |
dc.contributor.author | Musat, Alexandra | |
dc.contributor.author | Trebat-Leder, Sarah | |
dc.date.accessioned | 2017-04-07T16:55:37Z | |
dc.date.available | 2017-04-07T16:55:37Z | |
dc.date.issued | 2013-11 | |
dc.date.submitted | 2011-07 | |
dc.identifier.issn | 0026-9255 | |
dc.identifier.issn | 1436-5081 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/107942 | |
dc.description.abstract | Folsom, 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.publisher | Springer Vienna | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1007/s00605-013-0586-y | en_US |
dc.rights | Article 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.source | Springer Vienna | en_US |
dc.title | ℓ-Adic properties of partition functions | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Belmont, 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.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
dc.contributor.mitauthor | Belmont, Eva | |
dc.relation.journal | Monatshefte für Mathematik | en_US |
dc.eprint.version | Author's final manuscript | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dc.date.updated | 2016-05-23T12:08:48Z | |
dc.language.rfc3066 | en | |
dc.rights.holder | Springer-Verlag Wien | |
dspace.orderedauthors | Belmont, Eva; Lee, Holden; Musat, Alexandra; Trebat-Leder, Sarah | en_US |
dspace.embargo.terms | N | en |
dc.identifier.orcid | https://orcid.org/0000-0003-3312-6665 | |
mit.license | PUBLISHER_POLICY | en_US |