Statistical distribution of the Stern sequence
Sandro Bettin, Sary Drappeau, Lukas Spiegelhofer
TL;DR
This paper proves that the Stern diatomic sequence follows a normal distribution asymptotically on a logarithmic scale, using complex moments and transfer operator analysis.
Contribution
It introduces a novel approach to analyze the distribution of the Stern sequence through complex moments and transfer operators.
Findings
Stern sequence is asymptotically normally distributed on a log scale
Use of complex moments to study sequence distribution
Analytic properties of transfer operators are key to the proof
Abstract
We prove that the Stern diatomic sequence is asymptotically distributed according to a normal law, on a logarithmic scale. This is obtained by studying complex moments, and the analytic properties of a transfer operator.
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