✦ LIBER ✦

On an Inequality of Erdős and Turán Concerning Uniform Distribution Modulo One, II

✍ Scribed by I.Z. Ruzsa

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 126 KB
Volume: 49
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1994.1082

No coin nor oath required. For personal study only.

✦ Synopsis

A famous inequality of Erdös and Turán estimates the discrepancy (\Delta) of a finite sequence of real numbers by the quantity (B=\min {K} K^{-1}+\sum{k=1}^{K-1}\left|\alpha_{k}\right| / k), where the (\alpha_{k}) are the Fourier coefficients. We investigate how bad this estimate can be. We prove that in the worst case (\Delta) is of order (B^{3 / 2}). 1994 Academic Press, Inc.

📜 SIMILAR VOLUMES

On A Problem of Erdős and Turán and Some

On A Problem of Erdős and Turán and Some Related Results

✍ N. Alon; M.N. Kolountzakis 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 315 KB

We employ the probabilistic method to prove a stronger version of a result of Helm, related to a conjecture of Erdos and Turan about additive bases of the positive integers. We show that for a class of random sequences of positive integers \(A\), which satisfy \(|A \cap[1, x]| \gg \sqrt{x}\) with pr