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On positive cosine sums
Published online by Cambridge University Press: 10 April 2007
Abstract
For α∈ (0,1) and x∈ [0,π, we define S0(x,α) = 1 and where Also, we set, for α∈ (0,1), where it is agreed that infØ =∞. It is shown in this paper that and 8≤ N(α)<∞ if α0<α<α*, where α*:=0.33542. . . is the unique solution α∈ (0,1) of the equation while α0= 0.308443. . . is the unique solution α∈ (0,1) of the equation In the case α*<α<1, this extends a result of Brown, Wang and Wilson (1993).
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 2 , March 2007 , pp. 219 - 232
- Copyright
- Copyright © Cambridge Philosophical Society 2007
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