Explicit bounds on the coefficients of modular polynomials and the size of X0(N)

Florian Breuer, Desirée Gijón Gómez, Fabien Pazuki*

*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

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Abstract

We give explicit upper and lower bounds on the size of the coefficients of the modular polynomials (Formula presented.) for the elliptic (Formula presented.) -function. These bounds make explicit the best previously known asymptotic bounds. We then give an explicit version of Silverman's Hecke points estimates. Finally, we give an asymptotic comparison between the Faltings height of the modular curve (Formula presented.) and the height of the modular polynomial (Formula presented.).

OriginalsprogEngelsk
Artikelnummere70020
TidsskriftProceedings of the London Mathematical Society
Vol/bind130
Udgave nummer1
Antal sider25
ISSN0024-6115
DOI
StatusUdgivet - 2025

Bibliografisk note

Funding Information:
The authors thank Pascal Autissier, Joe Silverman and Emmanuel Ullmo, for conversations around this topic at the occasion of the Hindry 65 conference in Bordeaux. They also thank Autissier for comments on an earlier version of the text. They thank Riccardo Pengo and Paolo Dolce for providing the reference [ 7 ]. They thank the referee for constructive feedback. The authors were supported by the IRN GandA (CNRS). The first author is supported by the Alexander\u2010von\u2010Humboldt Foundation. The third author is supported by ANR\u201020\u2010CE40\u20100003 Jinvariant.

Funding Information:
The authors thank Pascal Autissier, Joe Silverman and Emmanuel Ullmo, for conversations around this topic at the occasion of the Hindry 65 conference in Bordeaux. They also thank Autissier for comments on an earlier version of the text. They thank Riccardo Pengo and Paolo Dolce for providing the reference [7]. They thank the referee for constructive feedback. The authors were supported by the IRN GandA (CNRS). The first author is supported by the Alexander-von-Humboldt Foundation. The third author is supported by ANR-20-CE40-0003\u00A0Jinvariant.

Publisher Copyright:
© 2024 The Author(s). The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.

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