Disjointness of the Möbius Transformation and Möbius Function

2017/11/29 by El Houcein El Abdalaoui, Abdalaoui, El Houcein El, Igor E. Shparlinski +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1711.11062

openalex publication_date 2017/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the distribution of the sequence of elements of the discrete dynamical system generated by the Möbius transformation x ↦ (ax + b)/(cx + d) over a finite field of p elements. Motivated by a recent conjecture of P. Sarnak, we obtain nontrivial estimates of exponential sums with such sequences that imply that trajectories of this dynamical system are disjoined with the Möbius function.

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• On the Dynamical System Generated by the Möbius Transformation at Smooth Times

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