1. On problems of Erdös and Rudin.
- Author
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Mei-Chu Chang
- Subjects
- *
LEAST squares , *SET theory , *GRAPH theory , *MATHEMATICS - Abstract
A well-known conjecture of W. Rudin is that the set of squares is a ∧p-set for all p>4. In particular, this implies that for all ε>0, there exists a constant cϵ such that∫Π∑j=1keinj2λ4dx14⩽cϵk12+ϵfor any k distinct integers n1…nk. In this article we give a combinatorial interpretation of the inequality above in the spirit of \|q\|q sum and product sets along graphs as considered by P. Erdo¨s and E. Szemeredi (Studies in Pure Mathematics, pp. 213–218). We also show that the left-hand side of the inequality is bounded by Cϵk34(logk)148−ϵ. [Copyright &y& Elsevier]
- Published
- 2004
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