Explicit bounds on the coefficients of modular polynomials and the size of X0(N)$X_0(N)$

Abstract We give explicit upper and lower bounds on the size of the coefficients of the modular polynomials for the elliptic ‐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 and the height of the modular polynomial .

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Publication Details

Journal
Proceedings of the London Mathematical Society
Published
2024-12-28
DOI
https://doi.org/10.1112/plms.70020
Citations
1
Primary Topic
Algebraic Geometry and Number Theory
Type
article
Field-Weighted Citation Impact
1.01

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article

Explicit bounds on the coefficients of modular polynomials and the size of X0(N)$X_0(N)$

Florian Breuer, Fabien Pazuki, Desirée Gijón Gómez
1 citations
Proceedings of the London Mathematical Society
Algebraic Geometry and Number Theory
1.01
article

Explicit bounds on the coefficients of modular polynomials and the size of X0(N)$X_0(N)$

Florian Breuer, Fabien Pazuki, Desirée Gijón Gómez
article en
1 citations

Abstract

Abstract We give explicit upper and lower bounds on the size of the coefficients of the modular polynomials for the elliptic ‐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 and the height of the modular polynomial .

Proceedings of the London Mathematical SocietyVol. 130(1)
University of Copenhagen (DK), University of Newcastle Australia (AU)
Agence Nationale de la Recherche, Centre National de la Recherche Scientifique
Openalex Percentile: Top 20%
Algebraic Geometry and Number Theory
1.01
DOIOpen Access PDFOpenAlex
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Explicit bounds on the coefficients of modular polynomials and the size of X0(N)$X_0(N)$ — Florian Breuer, Fabien Pazuki, et al. · Proceedings of the London Mathematical Society (2024) | TGRS Research Map | TGRS