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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 $$x \mapsto (ax + b)/(cx + d)$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research in the Mathematical Sciences Springer Journals

Disjointness of the Möbius Transformation and Möbius Function

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Publisher
Springer Journals
Copyright
Copyright © 2019 by Springer Nature Switzerland AG
Subject
Mathematics; Mathematics, general; Applications of Mathematics; Computational Mathematics and Numerical Analysis
eISSN
2197-9847
DOI
10.1007/s40687-019-0180-6
Publisher site
See Article on Publisher Site

Abstract

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

Journal

Research in the Mathematical SciencesSpringer Journals

Published: Feb 7, 2019

References