On the Dynamical System Generated by the Möbius Transformation at Smooth Times

2025/07/16 by Mérai, László, Shparlinski, Igor E. · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2507.12160

Abstract

We study the distribution of the sequence of the first N elements of the discrete dynamical system generated by the Möbius transformation x ↦ (αx + β)/(γx + 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.

Citations

• Exponential Sums with Sparse Polynomials and Distribution of the Power Generator
• Distribution of recursive matrix pseudorandom number generator modulo prime powers
• On the Dynamical System Generated by the Möbius transformation at Prime Times
• Disjointness of the Möbius Transformation and Möbius Function
• Pseudorandom Numbers and Hash Functions from Iterations of Multivariate Polynomials
• Multivariate Permutation Polynomial Systems and Nonlinear Pseudorandom Number Generators

Cited by

• Character sums of Division polynomials twisted by multiplicative functions

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