Heights on the finite projective line
Number Theory
2016-12-30 v1 Combinatorics
Abstract
Define the height function h(a) = min{k+(ka\mod p): k=1,2,...,p-1} for a = 0,1,...,p-1. It is proved that the height has peaks at p, (p+1)/2, and (p+c)/3, that these peaks occur at a= [p/3], (p-3)/2, (p-1)/2, [2p/3], p-3,p-2, and p-1, and that h(a) \leq p/3 for all other values of a.
Keywords
Cite
@article{arxiv.math/0703646,
title = {Heights on the finite projective line},
author = {Melvyn B. Nathanson},
journal= {arXiv preprint arXiv:math/0703646},
year = {2016}
}
Comments
10 pages, 1 figure