On the order of unimodular matrices modulo integers
Number Theory
2015-06-26 v1 Chaotic Dynamics
Abstract
Assuming the Generalized Riemann Hypothesis, we prove the following: If b is an integer greater than one, then the multiplicative order of b modulo N is larger than N^(1-\epsilon) for all N in a density one subset of the integers. If A is a hyperbolic unimodular matrix with integer coefficients, then the order of A modulo p is greater than p^(1-\epsilon) for all p in a density one subset of the primes. Moreover, the order of A modulo N is greater than N^(1-\epsilon) for all N in a density one subset of the integers.
Cite
@article{arxiv.math/0202053,
title = {On the order of unimodular matrices modulo integers},
author = {P. Kurlberg},
journal= {arXiv preprint arXiv:math/0202053},
year = {2015}
}
Comments
12 pages