On the Oesterl�-Masser conjecture

Stewart, C. L.; Tijdeman, R.

doi:10.1007/bf01294603

Cited by 82 publications

(106 citation statements)

References 5 publications

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“…This improves the result of Stewart and Tijdeman [9]. The value of l comes from an asymptotic bound for the packing density of spheres.…”

supporting

confidence: 53%

A Lower Bound in the abc Conjecture

Frankenhuysen

2000

Journal of Number Theory

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We show that there exists an infinite sequence of sums P: a+b=c of rational integers with large height compared to the radical:-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 . Academic PressKey Words: abc conjecture; good abc examples; the error term in the abc conjecture; sphere packing in n dimensions.

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“…This improves the result of Stewart and Tijdeman [9]. The value of l comes from an asymptotic bound for the packing density of spheres.…”

supporting

confidence: 53%

A Lower Bound in the abc Conjecture

Frankenhuysen

2000

Journal of Number Theory

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“…By means of the theory of logarithmic forms Stewart and Tijdeman [43] and Stewart and Yu [44], [45] obtained upper bounds for c as a function of N (a, b, c). The best known upper bounds are due to Stewart and Yu [45].…”

mentioning

confidence: 99%

“…The conjecture has many profound consequences; cf. [1], [6], [9], [13], [16], [19], [28], [29], [34], [35], [37], [43], [47], [48] and the references given there.…”

mentioning

confidence: 99%

On the abc conjecture in algebraic number fields

Győry

2008

Acta Arith.

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On the abc conjecture in algebraic number fields by K. Győry (Debrecen)To Professor W. M. Schmidt on his 75th birthdayIn our paper we obtain new, effective results (cf. Theorems 1 and 2 in Section 3) towards the truth of the uniform abc conjecture in number fields. Our theorems improve upon the earlier estimates established in this direction. Our Theorems 1 and 2 are deduced from some recent explicit results of Yu and the author [24] (cf. Theorem A in Section 2) concerning S-unit equations. Our proofs (cf. Section 4) depend ultimately on the best known estimates for linear forms in logarithms of algebraic numbers.

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“…An unconditional result in the direction of the abc conjecture has been obtained in 1986 by Stewart and Tijdeman [66] using lower bounds for linear combinations of logarithms, in the complex case as well as in the p-adic case: log c Ä ÄR 15 with an absolute constant Ä. This estimate has been refined by Stewart and Yukunrui, who proved in 1991 [67]: for any " > 0 and for c sufficiently large in terms of ",…”

Section: Abc Conjecturementioning

confidence: 93%