On Λ(p)-subsets of squares |
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Authors: | J. Bourgain |
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Affiliation: | (1) IHES, 35, Route de Chartres, Bures-sur-Yvette, France |
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Abstract: | This paper is a follow up of [B1]. It is shown that the sequence of squares {n 2|n=1, 2, ...} contains Λ(p)-subsets of “maximal density”, for any givenp>4. The proof is based on the probabilistic method developed in [B1] and a precise estimate of the Λ(p)-constant for the sequence of squares itself. Analogues of this phenomenon are obtained for other arithmetic sets, such as the sequence ofkth powers {n k |n=1, 2, ...} or the sequence of prime numbers. Sections 2 and 3 of the paper are of independent interest to orthogonal system theory. |
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