On the abc conjecture, II

On the abc conjecture, II

C. L. Stewart and Kunrui Yu

Source: Duke Math. J. Volume 108, Number 1 (2001), 169-181.

Abstract

Let x, y, and z be coprime positive integers with x+y=z. In this paper we give upper bounds for z in terms of the greatest square-free factor of xyz.

Related Works:

See also: C. L. Stewart, Kunrui Yu. On the abc conjecture. Math. Ann. Vol. 291, No. 2 (1991), p. 225-230.

Mathematical Reviews (MathSciNet): MR1129361

Primary Subjects: 11D75

Secondary Subjects: 11J25, 11J86

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.

If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1091737127
Mathematical Reviews number (MathSciNet): MR1831823
Digital Object Identifier: doi:10.1215/S0012-7094-01-10815-6
Zentralblatt MATH identifier: 1036.11032

back to Table of Contents

References

A. Baker, ``Logarithmic forms and the $abc$-conjecture'' in Number Theory (Eger, Hungary, 1996), de Gruyter, Berlin, 1998, 37--.

Mathematical Reviews (MathSciNet): MR1628831

C. L. Stewart and K. Yu, On the $abc$ conjecture, Math. Ann. 291 (1991), 225--230. MR 92k:11037

Mathematical Reviews (MathSciNet): MR1129361

Digital Object Identifier: doi:10.1007/BF01445201

P. Vojta, Diophantine Approximations and Value Distribution Theory, Lecture Notes in Math. 1239, Springer, Berlin, 1987. MR 91k:11049

Mathematical Reviews (MathSciNet): MR883451

M. Waldschmidt, A lower bound for linear forms in logarithms, Acta Arith. 37 (1980), 257--283. MR 82h:10049

Mathematical Reviews (MathSciNet): MR598881

K. Yu, Linear forms in $p$-adic logarithms, II, Compositio Math. 74 (1990), 15--113. MR 91h:11065a

Mathematical Reviews (MathSciNet): MR1055245

--. --. --. --., $p$-adic logarithmic forms and group varieties, I, J. Reine Angew. Math. 502 (1998), 29--92. MR 99g:11092

Mathematical Reviews (MathSciNet): MR1647551

--. --. --. --., $p$-adic logarithmic forms and group varieties, II, Acta Arith. 89 (1999), 337--378. MR 2000e:11097

Mathematical Reviews (MathSciNet): MR1703864

previous :: next