Average liar count for degree-2 Frobenius pseudoprimes
Number Theory
2020-04-07 v2
Abstract
In this paper we obtain lower and upper bounds on the average number of liars for the Quadratic Frobenius Pseudoprime Test of Grantham, generalizing arguments of Erd\H{o}s and Pomerance, and Monier. These bounds are provided for both Jacobi symbol plus and minus cases, providing evidence for the existence of several challenge pseudoprimes.
Cite
@article{arxiv.1707.05002,
title = {Average liar count for degree-2 Frobenius pseudoprimes},
author = {Andrew Fiori and Andrew Shallue},
journal= {arXiv preprint arXiv:1707.05002},
year = {2020}
}
Comments
19 pages, published in Mathematics of Computation, revised version fixes typos and made a minor correction to the proof of Lemma 18 (result remains unchanged)