Result: Negative values of cosine sums

Title:
Negative values of cosine sums
Authors:
Imre Z. Ruzsa
Source:
Acta Arithmetica. 111:179-186
Publisher Information:
Institute of Mathematics, Polish Academy of Sciences, 2004.
Publication Year:
2004
Subject Terms:
Other combinatorial number theory, Trigonometric polynomials, inequalities, extremal problems, 0103 physical sciences, Exponential sums and character sums, 0101 mathematics, 01 natural sciences
Document Type:
Academic journal Article
File Description:
application/xml
Language:
English
ISSN:
1730-6264
0065-1036
DOI:
10.4064/aa111-2-6
Access URL:
https://www.impan.pl/shop/publication/transaction/download/product/82437?download.pdf
https://zbmath.org/2092434
https://doi.org/10.4064/aa111-2-6
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-aa111-2-6
https://eudml.org/doc/278427
https://ui.adsabs.harvard.edu/abs/2004AcAri.111..179R/abstract
https://www.impan.pl/en/publishing-house/journals-and-series/acta-arithmetica/all/111/2/82437/negative-values-of-cosine-sums
Accession Number:
edsair.doi.dedup.....66b6a98c5f28adb9617c16f03e9f822f
Database:
OpenAIRE

Further Information

In this paper the author studies the so-called ``Chowla's cosine problem'' [see J. Reine Angew. Math. 217, 128--132 (1965; Zbl 0127.02104)]. From the introduction: Let \(A\) be a finite set of positive integers, \(|A|=n\), and write \(f(x)= \sum_{a\in A}\cos ax\). Since \(f(0)>0\) and \(\int_0^{2\pi} f(x)\,dx=0\), we have \(\min f(x)