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Gaps in the Spectrum of Heights of Projective Points

Kevin O'Bryant
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Abstract

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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Kevin O'Bryant. 2007-03-21. Gaps in the Spectrum of Heights of Projective Points. https://arxiv.org/abs/math/0703625

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