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Heights of CM Points on Complex Affine Curves

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Abstract

In this note we show that, assuming the generalized Riemann hypothesis for quadratic imaginary fields, an irreducible algebraic curve in ℂŋ is modular if and only if it contains a CM point of sufficiently large height. This is an effective version of a theorem of Edixhoven.

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Authors and Affiliations

  1. UMR Mathematiques, Universite Denis Diderot, Paris 7, France

    Florian Breuer

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  1. Florian Breuer
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Breuer, F. Heights of CM Points on Complex Affine Curves. The Ramanujan Journal 5, 311–317 (2001). https://doi.org/10.1023/A:1012982812988

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