Near miss $abc$-triples in general number fields

Abstract

Masser and others have constructed sequences of ‘‘near miss’’ $abc$-triples, i.e., triples of relatively prime rational integers $(a, b, c)$ that asymptotically come close to violating the inequality that appears in the $abc$ Conjecture. In the present paper, we show various partial generalizations of Masser’s result to arbitrary number fields.