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arXiv · 2507.12160

On the Dynamical System Generated by the M\"obius Transformation at Smooth Times

László Mérai·Igor E. Shparlinski
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Abstract

We study the distribution of the sequence of the first $N$ elements of the discrete dynamical system generated by the M\"obius transformation $x \mapsto (\alpha x + \beta)/(\gamma x + \delta)$ over a finite field of $p$ elements at the moments of time that correspond to $Q$-smooth numbers, that is, to numbers composed out of primes up to $Q$. In particular, we obtain nontrivial estimates of exponential sums with such sequences.

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László Mérai, Igor E. Shparlinski. 2025-07-16. On the Dynamical System Generated by the M\"obius Transformation at Smooth Times. https://arxiv.org/abs/2507.12160

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