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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