Helfgott, Harald Andrés

[["dc.bibliographiccitation.firstpage","3593"],["dc.bibliographiccitation.issue","8"],["dc.bibliographiccitation.journal","Proceedings of the American Mathematical Society"],["dc.bibliographiccitation.lastpage","3602"],["dc.bibliographiccitation.volume","143"],["dc.contributor.author","Gill, Nick"],["dc.contributor.author","Helfgott, Harald Andrés"],["dc.contributor.author","Rudnev, Misha"],["dc.date.accessioned","2017-09-07T11:54:22Z"],["dc.date.available","2017-09-07T11:54:22Z"],["dc.date.issued","2015"],["dc.description.abstract","There is a parallelism between growth in arithmetic combinatorics and growth in a geometric context. While, over R or C, geometric statements on growth often have geometric proofs, what little is known over finite fields rests on arithmetic proofs. We discuss strategies for geometric proofs of growth over finite fields, and show that growth can be defined and proven in an abstract projective plane – even one with weak axioms."],["dc.identifier.doi","10.1090/proc/12309"],["dc.identifier.gro","3146549"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4331"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","American Mathematical Society (AMS)"],["dc.relation.eissn","1088-6826"],["dc.relation.issn","0002-9939"],["dc.title","On growth in an abstract plane"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","135"],["dc.bibliographiccitation.issue","01"],["dc.bibliographiccitation.journal","Mathematika"],["dc.bibliographiccitation.lastpage","145"],["dc.bibliographiccitation.volume","57"],["dc.contributor.author","Helfgott, Harald Andrés"],["dc.contributor.author","Rudnev, Misha"],["dc.date.accessioned","2017-09-07T11:54:25Z"],["dc.date.available","2017-09-07T11:54:25Z"],["dc.date.issued","2011"],["dc.description.abstract","Let P=A×A⊂𝔽p×𝔽p, p a prime. Assume that P=A×A has n elements, n