Title:
Problems in combinatorial number theory

dc.contributor.advisor Wick, Brett D.
dc.contributor.author Amirkhanyan, Gagik M.
dc.contributor.committeeMember Lacey, Michael T.
dc.contributor.committeeMember Lubinsky, Doron
dc.contributor.committeeMember Geronimo, Jeff
dc.contributor.committeeMember Bilyk, Dmitriy
dc.contributor.department Mathematics
dc.date.accessioned 2014-05-22T15:31:39Z
dc.date.available 2014-05-22T15:31:39Z
dc.date.created 2014-05
dc.date.issued 2014-04-02
dc.date.submitted May 2014
dc.date.updated 2014-05-22T15:31:39Z
dc.description.abstract The dissertation consists of two parts. The first part is devoted to results in Discrepancy Theory. We consider geometric discrepancy in higher dimensions (d > 2) and obtain estimates in Exponential Orlicz Spaces. We establish a series of dichotomy-type results for the discrepancy function which state that if the L¹ norm of the discrepancy function is too small (smaller than the conjectural bound), then the discrepancy function has to be very large in some other function space.The second part of the thesis is devoted to results in Additive Combinatorics. For a set with small doubling an order-preserving Freiman 2-isomorphism is constructed which maps the set to a dense subset of an interval. We also present several applications.
dc.description.degree Ph.D.
dc.format.mimetype application/pdf
dc.identifier.uri http://hdl.handle.net/1853/51865
dc.language.iso en_US
dc.publisher Georgia Institute of Technology
dc.subject Geometric discrepancy
dc.subject Additive energy, Freiman isomorphism
dc.subject.lcsh Combinatorial number theory
dc.subject.lcsh Irregularities of distribution (Number theory)
dc.subject.lcsh Additive combinatorics
dc.title Problems in combinatorial number theory
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.corporatename College of Sciences
local.contributor.corporatename School of Mathematics
relation.isOrgUnitOfPublication 85042be6-2d68-4e07-b384-e1f908fae48a
relation.isOrgUnitOfPublication 84e5d930-8c17-4e24-96cc-63f5ab63da69
thesis.degree.level Doctoral
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