Arithmetic progressions in sumsets

BJ Green

Research output: Contribution to journalArticle (Academic Journal)

43 Citations (Scopus)

Abstract

We prove several results concerning arithmetic progressions in sets of integers. Suppose, for example, that alpha and beta are positive reals, that N is a large prime and that C, D subset of or equal to Z/NZ have sizes gammaN and deltaN respectively. Then the sumset C + D contains an AP of length at least e(crootlog N), where c > 0 depends only on gamma and delta. In deriving these results we introduce the concept of hereditary non-uniformity (HNU) for subsets of Z/NZ, and prove a structural result for sets with this property.
Translated title of the contributionArithmetic progressions in sumsets
Original languageEnglish
Pages (from-to)584 - 597
JournalGeometric and Functional Analysis
Volume12 (3)
Publication statusPublished - 2002

Bibliographical note

Publisher: Birkhauser Verlag Ag
Other identifier: IDS Number: 587BT

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