Good abc Examples Over Number Fields

摘要

Let k be a number field. The authors will (implicitly) construct an infinitesequence of points P = (a: b: c) and P(squared)(k) on the line a + b = c, with large height compared to the radical: h(sup k)(P) > or = r(sub k)(P) + 4(square root of 2)(square root of h(sub k)(P)/log h(sub k)(P)). The authors result improves the result of Stewart and Tijdeman, who give this construction for k = Q.