# On extreme values for the Sudler product of quadratic irrationals

@inproceedings{Hauke2021OnEV, title={On extreme values for the Sudler product of quadratic irrationals}, author={Manuel Hauke}, year={2021} }

Given a real number α and a natural number N , the Sudler product is defined by PN (α) = ∏N r=1 2 ∣∣sin(π (rα))∣∣ . Denoting by Fn the n–th Fibonacci number and by φ the Golden Ratio, we show that for Fn−1 6 N < Fn, we have PFn−1(φ) 6 PN (φ) 6 PFn−1(φ) and minN>1 PN (φ) = P1(φ), thereby proving a conjecture of Grepstad, Kaltenböck and Neumüller. Furthermore, we find closed expressions for lim infN→∞ PN (φ) and lim supN→∞ PN (φ) N whose numerical values can be approximated arbitrarily well. We…

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## 2 Citations

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