Disjointness of the Möbius Transformation and Möbius Function

Disjointness of the Möbius Transformation and Möbius Function

We study the distribution of the sequence of elements of the discrete dynamical system generated by the Möbius transformation x ↦ ( a x + b ) / ( c x + 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 s...

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Veröffentlicht in:Research in the mathematical sciences 2019-03, Vol.6 (1), p.1-14, Article 17
Hauptverfasser: El Abdalaoui, El Houcein, Shparlinski, Igor E.
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Dynamical systems
Fields (mathematics)
Geometric transformation
Mathematics
Mathematics and Statistics
Number theory
Sequences
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Zusammenfassung:We study the distribution of the sequence of elements of the discrete dynamical system generated by the Möbius transformation x ↦ ( a x + b ) / ( c x + 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.
ISSN:2522-0144
2197-9847
DOI:10.1007/s40687-019-0180-6