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Notes on Pólya's and Turán's hypotheses concerning Liouville's factor

✍ Scribed by Norbert Wiener; Aurel Wintner

Book ID
112907840
Publisher
Springer Milan
Year
1957
Tongue
Italian
Weight
363 KB
Volume
6
Category
Article
ISSN
0009-725X

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On an Inequality of Erdős and Turán Conc
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✍ I.Z. Ruzsa 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 126 KB

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