On extreme values for the Sudler product of quadratic irrationals

Abstract

For a real number $\alpha $ and a natural number $N$, the Sudler product is defined by $P_N(\alpha ) = \prod _{r=1}^{N} 2 \lvert \sin (\pi r\alpha )\rvert $. Denoting by $F_n$ the $n$th Fibonacci number and by $\phi $ the Golden Ratio, we show that for $F