A positive proportion of locally soluble quartic Thue equations are globally insoluble

DOI10.1017/S0305004121000554zbMath1504.11054arXiv2002.00548OpenAlexW3207527788MaRDI QIDQ5097475

Shabnam Akhtari

Publication date: 24 August 2022

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.00548

zbMATH Keywords

Thue equationsbinary quartic forms

Mathematics Subject Classification ID

Counting solutions of Diophantine equations (11D45) Cubic and quartic Diophantine equations (11D25)

Cites Work

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• Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves
• The number of points on a singular curve over a finite field
• On Thue's equation
• REPRESENTATION OF SMALL INTEGERS BY BINARY FORMS
• On the Number of Solutions of Polynomial Congruences and Thue Equations
• A positive proportion of Thue equations fail the integral Hasse principle
• The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point
• On the density of discriminants of cubic fields. II
• Finiteness Theorems for Binary Forms with Given Discriminant

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