On the multiplicative group generated by two primes in $\mathbf{Z}/Q\mathbf{Z}$

Péter P. Varjú

On the multiplicative group generated by two primes in $\mathbf{Z}/Q\mathbf{Z}$

Number Theory 2022-08-25 v2 Dynamical Systems

Authors: Péter P. Varjú

Abstract

We study the action of the multiplicative group generated by two prime numbers in $\mathbf{Z}/Q\mathbf{Z}$ . More specifically, we study returns to the set $([-Q^\varepsilon,Q^\varepsilon]\cap \mathbf{Z})/Q\mathbf{Z}$ . This is intimately related to the problem of bounding the greatest common divisor of $S$ -unit differences, which we revisit. Our main tool is the $S$ -adic subspace theorem.

Keywords

prime numbers prime number theory

Cite

@article{arxiv.2104.04367,
  title  = {On the multiplicative group generated by two primes in $\mathbf{Z}/Q\mathbf{Z}$},
  author = {Péter P. Varjú},
  journal= {arXiv preprint arXiv:2104.04367},
  year   = {2022}
}

Comments

14 pages, final accepted version, revision based on referee's comments, new title, improved presentation, to appear in Analysis at Large: Dedicated to the Life and Work of Jean Bourgain

On the multiplicative group generated by two primes in $\mathbf{Z}/Q\mathbf{Z}$

Abstract

Keywords

Cite

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