HEIGHTS ON THE FINITE PROJECTIVE LINE
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Publication:3622216
DOI10.1142/S179304210900192XzbMATH Open1177.11009arXivmath/0703646OpenAlexW2077379304MaRDI QIDQ3622216
Publication date: 28 April 2009
Published in: International Journal of Number Theory (Search for Journal in Brave)
Abstract: Define the height function h(a) = min{k+(kamod 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.
Full work available at URL: https://arxiv.org/abs/math/0703646
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Paths and cycles (05C38) Finite fields and commutative rings (number-theoretic aspects) (11T99) Heights (11G50) Congruences; primitive roots; residue systems (11A07)
Cites Work
Related Items (3)
Title not available (Why is that?) ⋮ Nathanson heights in finite vector spaces ⋮ Projective metric number theory
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