Disjointness of the Möbius Transformation and Möbius Function

  • El Houcein El Abdalaoui
  • Igor E. ShparlinskiEmail author


We study the distribution of the sequence of elements of the discrete dynamical system generated by the Möbius transformation \(x \mapsto (ax + b)/(cx + d)\) 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.


Möbius function Möbius transformation Möbius disjointness Exponential sums over primes 

Mathematics Subject Classification

11L07 11N60 11T23 37P05 



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Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Raphaël SalemUniversité de Rouen NormandieSaint-Étienne-du-RouvrayFrance
  2. 2.School of Mathematics and StatisticsUniversity of New South WalesSydneyAustralia

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