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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