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- W3149919682 abstract "There is an extensive literature on the asymptotic order of Sudler's trigonometric product $P_N (alpha) = prod_{n=1}^N |2 sin (pi n alpha)|$ for fixed or for typical values of $alpha$. In the present paper we establish a structural result, which for a given $alpha$ characterizes those $N$ for which $P_N(alpha)$ attains particularly large values. This characterization relies on the coefficients of $N$ in its Ostrowski expansion with respect to $alpha$, and allows us to obtain very precise estimates for $max_{1 le N leq M} P_N(alpha)$ and for $sum_{N=1}^M P_N(alpha)^c$ in terms of $M$, for any $c>0$. Furthermore, our arguments give a natural explanation of the fact that the value of the hyperbolic volume of the complement of the figure-eight knot appears generically in results on the asymptotic order of the Sudler product and of the Kashaev invariant." @default.
- W3149919682 created "2021-04-13" @default.
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- W3149919682 date "2023-04-12" @default.
- W3149919682 modified "2023-09-30" @default.
- W3149919682 title "Maximizing Sudler products via Ostrowski expansions and cotangent sums" @default.
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- W3149919682 doi "https://doi.org/10.2140/ant.2023.17.667" @default.
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