Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  116.04703
Autor:  Erdös, Pál
Title:  On trigonometric sums with gaps (In English)
Source:  Publ. Math. Inst. Hung. Acad. Sci., Ser. A 7, 37-42 (1962).
Review:  The main result in this paper is the following theorem:
Theorem 1. Let n1 < n2 < ··· be an infinite sequence of integers satisfying nk+1 > nk (1+ck /k ½), where ck ––> oo. Then

limN = oo |Et \left{sumk = 1N (\cos 2\pi nk (t-\thetak)) < \omega N ½ \right} | = {1 \over 2\pi} int-oooo e-u2/2 du

(|Et{.}| denotes the Lebesgue measure of the set in question).
Reviewer:  Y.M.Chen
Classif.:  * 42A05 Trigonometric polynomials
                   11L03 Trigonometric and exponential sums, general
Index Words:  approximation and series expansion

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