UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

A three dimensional set of limit points related to the abc Conjecture Simpson, Reginald M.


We study the limit points Q' of a three-dimensional set Q which encodes the reciprocal quality of abc triples as the components of a vector of the form (log Rad a, log Rad b, log Rad c) / log c. We establish that if the abc Conjecture holds, Q' is contained in a heptahedron. Unconditionally, we establish the existence of a subset of Q' with non-zero measure. We determine the implications of previous research on related problems involving limit points of abc triples in one-dimensional sets on Q' and discuss possible avenues for future study.

Item Citations and Data


Attribution-NonCommercial-NoDerivatives 4.0 International