On Trigonometric Sums with Gaps
نویسنده
چکیده
A well known theorem states as follows :' Let ni < n2 <. . ., nk+1 / nk > A > 1 be an infinite sequence of real numbers and S (ak + bk) a divergent series satisfying k=1 Then denotes the Lebesgue measure of the set in question. It seems likely that the Theorem remains true if it is not assumed that the n k are integers. On the other hand if nk ,f-n,.-1 is an arbitrary sequence of integers it is easy to construct examples which show that (1) is not enough 1 R. SALEM and A. ZYGMUND : "On lacunary trigonometrie series I. and II .", Proc. For the history of the problem see M. KAC : "Probability methods in analysis anti number theory" .
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