On Distribution of Solutions ofS-Unit Equations

Poe, M.

doi:10.1006/jnth.1997.2046

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“…By a very different method, Bombieri, Mueller and Poe [3] showed that if G has rank r and is contained in a number field of degree d, then (2.21) has at most d 9r 2 125r 2 solutions. They obtained their result by extending an idea of Poe [23] to a general "cluster principle" entailing that the solutions of (2.21) can be divided into clusters of solutions lying close together, and by combining this with an effective upper bound for the heights of the solutions of (2.21) obtained by means of lower bounds for linear forms in logarithms.…”

Section: Historymentioning

confidence: 99%

The Absolute Subspace Theorem and linear equations with unknowns from a multiplicative group

Evertse¹,

Schlickewei²

1999

Number Theory in Progress

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Section: Historymentioning

confidence: 99%

The Absolute Subspace Theorem and linear equations with unknowns from a multiplicative group

Evertse¹,

Schlickewei²

1999

Number Theory in Progress

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The Thirties

Narkiewicz

2012

Springer Monographs in Mathematics

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Unit Equations in Diophantine Number Theory

Evertse

Győry

2015

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Diophantine number theory is an active area that has seen tremendous growth over the past century, and in this theory unit equations play a central role. This comprehensive treatment is the first volume devoted to these equations. The authors gather together all the most important results and look at many different aspects, including effective results on unit equations over number fields, estimates on the number of solutions, analogues for function fields and effective results for unit equations over finitely generated domains. They also present a variety of applications. Introductory chapters provide the necessary background in algebraic number theory and function field theory, as well as an account of the required tools from Diophantine approximation and transcendence theory. This makes the book suitable for young researchers as well as experts who are looking for an up-to-date overview of the field.

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On Distribution of Solutions ofS-Unit Equations

Cited by 3 publications

References 3 publications

The Absolute Subspace Theorem and linear equations with unknowns from a multiplicative group

The Absolute Subspace Theorem and linear equations with unknowns from a multiplicative group

The Thirties

Unit Equations in Diophantine Number Theory

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