Borwein, Peter Benjamin; Erdélyi, Tamás; Ferguson, Ron; Lockhart, Richard On the zeros of cosine polynomials: solution to a problem of Littlewood. (English) Zbl 1186.11045 Ann. Math. (2) 167, No. 3, 1109-1117 (2008). The problem in the title states: “If the \(n_j\) are distinct integers, what is the lower bound on the number of real zeros of \(\sum^N_{j=1} \cos(n_j\theta)\)? Possibly \(N-1\), or not much less.” The authors prove the following theorem, which shows that \(N-1\) is not correct. There exists such a cosine polynomial whose number of zeros in the interval \([-\pi, \pi)\) is \(O(N^{5/6}\log N)\). Reviewer: Tom M. Apostol (Pasadena) Cited in 1 ReviewCited in 16 Documents MSC: 11L03 Trigonometric and exponential sums (general theory) 42A05 Trigonometric polynomials, inequalities, extremal problems PDFBibTeX XMLCite \textit{P. B. Borwein} et al., Ann. Math. (2) 167, No. 3, 1109--1117 (2008; Zbl 1186.11045) Full Text: DOI Link