Commentarii Mathematici Helvetici

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Volume 94, Issue 2, 2019, pp. 241–271
DOI: 10.4171/CMH/460

Published online: 2019-04-17

Statistical distribution of the Stern sequence

Sandro Bettin[1], Sary Drappeau[2] and Lukas Spiegelhofer[3]

(1) Università di Genova, Italy
(2) Aix-Marseille Université, Marseille, France
(3) Technische Universität Wien, Austria

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.

Keywords: Stern diatomic sequence, transfer operator, central limit theorem

Bettin Sandro, Drappeau Sary, Spiegelhofer Lukas: Statistical distribution of the Stern sequence. Comment. Math. Helv. 94 (2019), 241-271. doi: 10.4171/CMH/460