Arithmetic structures in random sets

Mariah Hamel; Izabella Laba

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Arithmetic structures in random sets

Mariah Hamel·Izabella Laba

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Abstract

We extend two well-known results in additive number theory, Sárközy's theorem on square differences in dense sets and a theorem of Green on long arithmetic progressions in sumsets, to subsets of random sets of asymptotic density 0. Our proofs rely on a restriction-type Fourier analytic argument of Green and Green-Tao.

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Mariah Hamel, Izabella Laba. 2007-03-26. Arithmetic structures in random sets. https://arxiv.org/abs/math/0703749

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