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A Lower Bound in the abc Conjecture

✍ Scribed by Machiel Van Frankenhuysen

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 91 KB
Volume: 82
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1999.2484

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✦ Synopsis

We show that there exists an infinite sequence of sums P: a+b=c of rational integers with large height compared to the radical: h(P) r(P)+4K l -h(P)Âlog h(P) with K l =2 lÂ2 4 -2?Âe>1.517 for l=0.5990. This improves the result of Stewart and Tijdeman [9]. The value of l comes from an asymptotic bound for the packing density of spheres. We formulate our result such that improved knowledge of l immediately improves the value of K l .

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