The proportion of plane cubic curves over ℚ that everywhere locally have a point

DOI10.1142/S1793042116500664zbMath1341.11033arXiv1311.5578MaRDI QIDQ2805971

Manjul Bhargava, Tom A. Fisher, John E. Cremona

Publication date: 13 May 2016

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.5578

zbMATH Keywords

local solubilityplane cubic curvesrandom Diophantine equations

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Elliptic curves over local fields (11G07)

Related Items (10)

On the distribution of equivalence classes of random symmetric p‐adic matrices ⋮ MANY CUBIC SURFACES CONTAIN RATIONAL POINTS ⋮ Most binary forms come from a pencil of quadrics ⋮ Everywhere local solubility for hypersurfaces in products of projective spaces ⋮ Fibrations with few rational points ⋮ The proportion of plane cubic curves over ℚ that everywhere locally have a point ⋮ Odd order obstructions to the Hasse principle on general K3 surfaces ⋮ Failures of weak approximation in families ⋮ The proportion of genus one curves over ℚ defined by a binary quartic that everywhere locally have a point ⋮ On the proportion of locally soluble superelliptic curves

Cites Work

• Mixed Hodge polynomials of character varieties. With an appendix by Nicholas M. Katz.
• The proportion of plane cubic curves over ℚ that everywhere locally have a point
• Algebraic Stacks Whose Number of Points over Finite Fields is a Polynomial
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