Statistics for fixed points of the self-power map
Number Theory
2018-06-06 v2
Abstract
The map x -> x^x modulo p is related to a variation of the digital signature scheme in a similar way to the discrete exponentiation map, but it has received much less study. We explore the number of fixed points of this map by a statistical analysis of experimental data. In particular, the number of fixed points can in many cases be modeled by a binomial distribution. We discuss the many cases where this has been successful, and also the cases where a good model may not yet have been found.
Keywords
Cite
@article{arxiv.1403.5548,
title = {Statistics for fixed points of the self-power map},
author = {Matthew Friedrichsen and Joshua Holden},
journal= {arXiv preprint arXiv:1403.5548},
year = {2018}
}
Comments
11 pages, 7 figures; replaced theoretical bounds with stronger ones from elsewhere, fixed some typos