# Arithmetic progressions in sumsets

@article{Green2002ArithmeticPI,
title={Arithmetic progressions in sumsets
},
author={B. Green},
journal={Geometric & Functional Analysis GAFA},
year={2002},
volume={12},
pages={584-597}
}
• B. Green
• Published 2002
• Mathematics
• Geometric & Functional Analysis GAFA
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 $C,D \subseteq {\Bbb Z}/N{\Bbb Z}$ have sizes $\gamma N$ and $\delta N$ respectively. Then the sumset C + D contains an AP of length at least $e^{c \sqrt{\rm log} N}$, where c > 0 depends only on $\gamma$ and $\delta$. In deriving these results we introduce the concept of hereditary non… Expand
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