Exponential sums and additive combinatorics

dc.contributor.advisor Shparlinski, Igor en_US Macourt, Simon en_US 2022-03-23T12:20:39Z 2022-03-23T12:20:39Z 2020 en_US
dc.description.abstract In this thesis we provide new results in additive combinatorics which in turn lead us to new bounds of certain exponential sums. We also use known bounds on exponential and character sums to give new results in additive combinatorics. Specifically we will see how bounds on some quantities from additive combinatorics appear naturally when trying to bound multilinear exponential sums. We then find applications to bounds of exponential sums of sparse polynomials. We also give new bounds for an analogue of the energy variant of the sum-product problem over arbitrary finite fields. en_US
dc.language English
dc.language.iso EN en_US
dc.publisher UNSW, Sydney en_US
dc.rights CC BY-NC-ND 3.0 en_US
dc.rights.uri en_US
dc.subject.other Additive combinatorics en_US
dc.subject.other Exponential sums en_US
dc.title Exponential sums and additive combinatorics en_US
dc.type Thesis en_US
dcterms.accessRights open access
dcterms.rightsHolder Macourt, Simon
dspace.entity.type Publication en_US
unsw.relation.faculty Science
unsw.relation.originalPublicationAffiliation Macourt, Simon, Mathematics & Statistics, Faculty of Science, UNSW en_US
unsw.relation.originalPublicationAffiliation Shparlinski, Igor, Mathematics & Statistics, Faculty of Science, UNSW en_US School of Mathematics & Statistics *
unsw.thesis.degreetype PhD Doctorate en_US
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