Arithmetic progressions in sumsets

BJ Green

Research output: Contribution to journalArticle (Academic Journal)peer-review

49 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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