On 𝑎𝑏𝑐 and discriminants

Masser, D.

doi:10.1090/S0002-9939-02-06589-9

On $abc$ and discriminants
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by D. W. Masser PDF

Proc. Amer. Math. Soc. 130 (2002), 3141-3150 Request permission

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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