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arXiv · 1411.2252

On the growth of Sudler's sine product at the golden rotation number

Paul Verschueren·Ben Mestel
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Abstract

We study the growth at the golden rotation number of Sudler's sine product. This sequence has been variously studied elsewhere as a skew product of sines, Birkhoff sum, q-Pochhammer symbol (on the unit circle), and restricted Euler function. In particular we study the Fibonacci decimation of the sequence, and prove that the renormalisation subsequence converges to a constant. From this we show rigorously that the growth is bounded by power laws. This provides the theoretical basis to explain recent experimental results reported by Knill and Tangerman (Self-similarity and growth in Birkhoff sums for the golden rotation. Nonlinearity, 24(11):3115-3127, 2011).

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Paul Verschueren, Ben Mestel. 2014-11-09. On the growth of Sudler's sine product at the golden rotation number. https://arxiv.org/abs/1411.2252

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