On the abc and the abcd conjectures

2024/06/07 by Héctor Pastén, Pasten, Hector, Rocío Sepúlveda-Manzo +1
Computer Science · Mathematics · #11J86 #11J97 #Advanced Algebra and Geometry #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #Primary: 11D75 #Rings, Modules, and Algebras #Secondary: 11J25

paper · pdf · doi:10.48550/arxiv.2406.05083

openalex publication_date 2024/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We revisit a subexponential bound for the abc conjecture due to the first author, and we establish a variation of it using linear forms in logarithms. As an application, we prove an unconditional subexponential bound towards the 4-terms abc conjecture under a suitable hypothesis on the size of the variables.

Related

• Probable Counterexamples of the ABC Conjecture
• Two Restricted ABC Conjectures
• The exceptional set in the abc conjecture
• A new lower bound in the conjecture
• A form of refined Roth's theorem and its application to the abc-conjecture