On Bhargava’s Heuristics for GL2(𝔽p)-Number Fields and the Number of Elliptic Curves of Bounded Conductor

DOI10.1080/10586458.2018.1537864zbMath1480.11066arXiv1610.09467OpenAlexW2915951908MaRDI QIDQ5003877

Michael Lipnowski

Publication date: 30 July 2021

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.09467

zbMATH Keywords

elliptic curveAtkin-Lehner involutionBhargava's mass heuristicsmod \(p\)-Galois representationweight 2 modular form

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Elliptic curves (14H52) Holomorphic modular forms of integral weight (11F11) Galois representations (11F80)

Cites Work

• \(p\)-torsion monodromy representations of elliptic curves over geometric function fields
• Effective equidistribution of eigenvalues of Hecke operators
• Serre's modularity conjecture. II
• On the modular representations of degree two of \(\text{Gal}({\overline {\mathbb Q}}/{\mathbb Q})\)
• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• Refined dimensions of cusp forms, and equidistribution and bias of signs
• Some Heuristics about Elliptic Curves
• The behavior of the Mordell-Weil group of elliptic curves
• The asymptotic growth of torsion homology for arithmetic groups
• Mass Formulae for Extensions of Local Fields, and Conjectures on the Density of Number Field Discriminants
• Répartition asymptotique des valeurs propres de l’opérateur de Hecke 𝑇_𝑝

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