Mathematics – Number Theory
Scientific paper
2007-03-26
Mathematics
Number Theory
22 pages
Scientific paper
We extend two well-known results in additive number theory, S\'ark\"ozy'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.
Hamel Mariah
Laba Izabella
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