Near miss $abc$-triples in general number fields

Abstract

A bstract . Masser and others have constructed sequences of ‘‘near miss’’ abc -triples, i.e., triples of relatively prime rational integers ð a ; b ; c Þ 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.