Heights on the finite projective line

Details Heights on the finite projective line Heights on the finite projective line

2007-03-22

arxiv.org/abs/math/0703646v1

Mathematics

Number Theory

10 pages, 1 figure

Scientific paper

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.

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