ABC implies the radicalized Vojta height inequality for curves

DOI10.1016/j.jnt.2006.03.010zbMath1197.11087arXiv0805.1729OpenAlexW1996214139MaRDI QIDQ2469148

Machiel van Frankenhuijsen

Publication date: 4 February 2008

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

Full work available at URL: https://arxiv.org/abs/0805.1729

zbMATH Keywords

Diophantine approximationRoth's theoremABC conjectureMordell's conjecturethe error term in the ABC conjecturetype of an algebraic numbereffective Mordellradicalized Vojta height inequality

Mathematics Subject Classification ID

Counting solutions of Diophantine equations (11D45) Diophantine inequalities (11D75) Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.) (11J97) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Related Items (5)

Lecture on the abc Conjecture and Some of Its Consequences ⋮ Integral points and orbits of endomorphisms on the projective plane ⋮ Two restricted ABC conjectures ⋮ Vojta's conjecture on rational surfaces and the \(abc\) conjecture ⋮ The exceptional set in Vojta’s conjecture for algebraic points of bounded degree

Cites Work

• The ABC conjecture implies Vojta's height inequality for curves
• On the Oesterlé-Masser conjecture
• Diophantine approximations and value distribution theory
• Topics in Nevanlinna theory
• A lower bound in the \(abc\) conjecture
• ON GALOIS EXTENSIONS OF A MAXIMAL CYCLOTOMIC FIELD
• POLYNOMIAL IDENTITIES AND HAUPTMODULN
• Rational approximations to algebraic numbers
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