General continued fractions and Thue equations

by Prof. I. Wakabayashi (Seikei University, Tokyo, Japan)

Friday 9 Dec 2011, 11:30 → 12:30 Asia/Kolkata

AG-77 (Colaba Campus)

In order to solve Thue equations, we need to obtain a lower bound for the size of solutions as well as an upper bound for it, and in order to obtain a lower bound we often use normal continued fractions. However, if we want solve a family of Thue equations of some type, normal continued fractions are not sufficient. Hence, we introduce general continued fractions, that is, continued fractions with rational partial quotients, and we generalize Legendre's theorem on principal convergents to general continued fractions. We give also applications to some families of Thue equations.