Gaps in the Spectrum of Heights of Projective Points

Details Gaps in the Spectrum of Heights of Projective Points Gaps in the Spectrum of Heights of Projective Points

2007-03-21

arxiv.org/abs/math/0703625v3

Integers 7 (2007), A38

Mathematics

Number Theory

6 pages, 1 figure (newest version is shorter and quantitative)

Scientific paper

Let r mod m be the least positive residue of r modulo m, and set the height of a pair (r,s) of integers, both relatively prime to m, to be the minimum over k, with 0 infinity, gcd(r_i,m_i)=gcd(s_i,m_i)=1, and m_i^{-1} h(m_i,r_i,s_i) --> x. The main result here is that SPECTRUM is the union of {0} and {1/k : k =1,2,...}.

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