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arXiv · 1711.11062

Disjointness of the M\"obius Transformation and M\"obius Function

El Houcein El Abdalaoui·Igor E. Shparlinski
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Abstract

We study the distribution of the sequence of elements of the discrete dynamical system generated by the M\"obius 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 M\"obius function.

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El Houcein El Abdalaoui, Igor E. Shparlinski. 2017-11-29. Disjointness of the M\"obius Transformation and M\"obius Function. https://arxiv.org/abs/1711.11062

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