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 contribution||Arithmetic progressions in sumsets|
|Pages (from-to)||584 - 597|
|Journal||Geometric and Functional Analysis|
|Publication status||Published - 2002|
Bibliographical notePublisher: Birkhauser Verlag Ag
Other identifier: IDS Number: 587BT