Anton Mosunov, Department of Pure Mathematics, University of Waterloo
“ESTIMATING THE NUMBER OF SOLUTIONS OF A THUE EQUATION: FURTHER ADVANCEMENTS”
Let F(x,y) be an irreducible binary form with integer coefficients of degree d ≥ 3. In 1987, Bombieri and Schmidt proved that the Thue equation |F(x,y)| = m for a positive integer m has at most c0d1+ω(m) solutions, where ω(m) denotes the number of prime divisors of m and c0 is a positive absolute constant. In this talk, we will discuss the result of Stewart, which states that ω(m) can be replaced with ω(g), where g is some large divisor of m. Also, we will mention a recent result of Thunder on the classification of solutions for large m.