Effective results for division points on curves in \(\mathbb{G}_m^2\)

DOI10.5802/jtnb.908zbMath1395.11104OpenAlexW2563663346MaRDI QIDQ888178

Attila Bérczes

Publication date: 4 November 2015

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5802/jtnb.908

zbMATH Keywords

curvesDiophantine equationseffective resultsdivision group of finitely generated groups

Mathematics Subject Classification ID

Varieties over global fields (11G35) Heights (11G50) Global ground fields in algebraic geometry (14G25)

Cites Work

• On the equation \(f(x)=y^ m\) over finitely generated domains
• Bounds for the solutions of norm form, discriminant form and index form equations in finitely generated integral domains
• Integral points on curves
• Division points on curves
• Approximate formulas for some functions of prime numbers
• Effective results for linear equations in two unknowns from a multiplicative division group
• Effective results for points on certain subvarieties of tori
• Effective finiteness theorems for polynomials with given discriminant and integral elements with given discriminant over finitely domains.
• Ideal membership in polynomial rings over the integers
• Effective results for unit equations over finitely generated integral domains
• Effective results for unit points on curves over finitely generated domains
• Effective results for Diophantine equations over finitely generated domains
• Report on Diophantine approximations
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