{"@context":"http://iiif.io/api/presentation/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/manifest.json","@type":"sc:Manifest","label":"On the Local-global Principle for Integral Apollonian","metadata":[{"label":"dc.description.sponsorship","value":"This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree."},{"label":"dc.format","value":"Monograph"},{"label":"dc.format.medium","value":"Electronic Resource"},{"label":"dc.identifier.uri","value":"http://hdl.handle.net/11401/76415"},{"label":"dc.language.iso","value":"en_US"},{"label":"dc.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.abstract","value":"Starting with three mutually tangent circles, in each of the two gaps we inscribe three circles, and then we inscribe three new circles into the newly generated circles, so on so forth? We obtain a packing of infinitely many circles, and we give a name Apollonian-3 packings.  It turns out there exist packings of this type with curvatures (1 over radius) all integers. I will discuss what we know about the integers arising as curvatures from these packings.  I will discuss the reduction theorem, the symmetry group, and a density one theorem towards the local-global conjecture."},{"label":"dcterms.available","value":"2017-09-20T16:50:11Z"},{"label":"dcterms.contributor","value":"Kontorovich, Alex"},{"label":"dcterms.creator","value":"Zhang, Xin"},{"label":"dcterms.dateAccepted","value":"2017-09-20T16:50:11Z"},{"label":"dcterms.dateSubmitted","value":"2017-09-20T16:50:11Z"},{"label":"dcterms.description","value":"Department of Mathematics."},{"label":"dcterms.extent","value":"47 pg."},{"label":"dcterms.format","value":"Application/PDF"},{"label":"dcterms.identifier","value":"http://hdl.handle.net/11401/76415"},{"label":"dcterms.issued","value":"2014-12-01"},{"label":"dcterms.language","value":"en_US"},{"label":"dcterms.provenance","value":"Made available in DSpace on 2017-09-20T16:50:11Z (GMT). No. of bitstreams: 1\nZhang_grad.sunysb_0771E_11905.pdf: 643514 bytes, checksum: 71060735c7147e2e03e44ba07897918e (MD5)\n  Previous issue date:    1"},{"label":"dcterms.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.subject","value":"Mathematics"},{"label":"dcterms.title","value":"On the Local-global Principle for Integral Apollonian"},{"label":"dcterms.type","value":"Dissertation"},{"label":"dc.type","value":"Dissertation"}],"description":"This manifest was generated dynamically","viewingDirection":"left-to-right","sequences":[{"@type":"sc:Sequence","canvases":[{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json","@type":"sc:Canvas","label":"Page 1","height":1650,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/10%2F80%2F36%2F108036732002497828007341917922531511078/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","height":1650,"width":1275,"service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/10%2F80%2F36%2F108036732002497828007341917922531511078","profile":"http://iiif.io/api/image/2/level2.json"}},"on":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json"}]}]}]}