On the Dynamical System Generated by the M\"obius Transformation at Smooth Times
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 (α x + β)/(γ x + δ) 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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