On the asymptotic behaviour of the sine product $\prod_{r=1}^n|2\sin(\pi r \alpha)|$
| Autor: | Grepstad, Sigrid, Kaltenböck, Lisa, Neumüller, Mario |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper we review recently established results on the asymptotic behaviour of the trigonometric product $P_n(\alpha) = \prod_{r=1}^n |2\sin \pi r \alpha|$ as $n\to \infty$. We focus on irrationals $\alpha$ whose continued fraction coefficients are bounded. Our main goal is to illustrate that when discussing the regularity of $P_n(\alpha)$, not only the boundedness of the coefficients plays a role; also their size, as well as the structure of the continued fraction expansion of $\alpha$, is important. Comment: To appear in: D. Bilyk, J. Dick, F. Pillichshammer (Eds.) Discrepancy theory, Radon Series on Computational and Applied Mathematics |
| Databáze: | arXiv |
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