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Special curves in modular surfaces

Part of: Discontinuous groups and automorphic forms Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  02 December 2021

Matteo Tamiozzo
Matteo Tamiozzo*
Affiliation:
Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, United Kingdom
*
e-mail: [email protected]
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Abstract

We show that geodesics in $\mathbf {H}$ attached to a maximal split torus or a real quadratic torus in $GL_{2, \mathbf {Q}}$ are the only irreducible algebraic curves in $\mathbf {H}$ whose image in $\mathbf {R}^2$ via the j-invariant is contained in an algebraic curve.

Keywords

Geodesicsmodular curvej-invariantfunctional transcendence

MSC classification

Primary: 11F03: Modular and automorphic functions
Secondary: 11J89: Transcendence theory of elliptic and abelian functions
Type
Article
Information
Canadian Mathematical Bulletin , Volume 66 , Issue 1 , March 2023 , pp. 1 - 18
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Copyright
© Canadian Mathematical Society, 2021

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Footnotes

The author’s research is supported by the ERC Grant 804176.

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