Disjointness of the Möbius Transformation and Möbius Function

Abstract

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.

References in corpus (1)

• Orbit structure and (reversing) symmetries of toral endomorphisms on rational lattices