CM-Points on Straight Lines

Bill Allombert (), Yuri Bilu () and Amalia Pizarro-Madariaga ()
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Bill Allombert: Université de Bordeaux, IMB
Yuri Bilu: Université de Bordeaux & CNRS, Institut de Mathématiques de Bordeaux
Amalia Pizarro-Madariaga: Universidad de Valparaíso, Instituto de Matemáticas

A chapter in Analytic Number Theory, 2015, pp 1-18 from Springer

Abstract: Abstract We prove that, with “obvious” exceptions, a CM-point ( j ( τ 1 ) , j ( τ 2 ) ) $$(j(\tau _{1}),j(\tau _{2}))$$ cannot belong to a straight line in ℂ 2 $$\mathbb{C}^{2}$$ defined over ℚ $$\mathbb{Q}$$ . This generalizes a result of Kühne, who proved this for the line x 1 + x 2 = 1 $$x_{1} + x_{2} = 1$$ .

Keywords: Ring Class Field; Imaginary Quadratic; Hilbert Class Polynomial; Recall Basic Facts; Special Subvarieties (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-22240-0_1

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