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On $abc$ and discriminants

Author(s): D. W. Masser
Journal: Proc. Amer. Math. Soc. 130 (2002), 3141-3150.
MSC (2000): Primary 11D61, 11P99, 11S99
Posted: April 17, 2002
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Abstract: We modify the $abc$-conjecture for number fields $K$ in order to make the support (like the height) well-behaved under field extensions. We show further that the exponent $\mu>1$ of the absolute value $D_K$ of the discriminant cannot be replaced by $\mu=1$, and even that an arbitrarily large power of $\log D_K$ must be present.

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Additional Information:

D. W. Masser
Affiliation: Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051 Basel, Switzerland
Email: masser@math.unibas.ch

DOI: 10.1090/S0002-9939-02-06589-9
PII: S 0002-9939(02)06589-9
Received by editor(s): June 4, 2001
Posted: April 17, 2002
Communicated by: David E. Rohrlich
Copyright of article: Copyright 2002, American Mathematical Society

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