On friable solutions of the equation \(a+b=c\) (Q2842338)
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scientific article; zbMATH DE number 6198183
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On friable solutions of the equation \(a+b=c\) |
scientific article; zbMATH DE number 6198183 |
Statements
13 August 2013
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\(abc\)-conjecture
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Generalized Riemann Hypothesis
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0.85628235
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0.8425452
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0.84012806
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0.8375168
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0.8360739
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On friable solutions of the equation \(a+b=c\) (English)
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The author studies the \(y\)--smooth solutions to the equation \(a+b=c\) (considered in the famous \(abc\)-conjecture), a positive integer \(x\) is called \(y\)-smooth if all its prime factors are \({}\leq y\). Such a study was also the subject of a recent work of \textit{J. C. Lagarias} and \textit{K. Soundararajan} [Proc. Lond. Math. Soc. (3) 104, No. 4, 770--798 (2012; Zbl 1270.11031)], who obtained asymptotic estimates the Generalized Riemann Hypothesis, GRH. Here the author obtains a more precise conditioned (again under GRH) estimate and which is valid in a larger domain. These results are also connected to papers by R. de La Bretèche and A. Granville and also by A. Hildebrand and G. Tenenbaum.
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