Academic Research: Dr. Ezra Waxman

Published at: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS

THUE EQUATIONS OVER C(T): THE COMPLETE SOLUTION OF A SIMPLE QUARTIC FAMILY

Abstract

We completely solve a simple quartic family of Thue equations over C(T). Specifically, we apply the ABC-theorem to find all solutions (x,y) ∈ C[T] × C[T] to the set of Thue equations F_λ(X,Y) = ξ, where ξ ∈ C^× and

F_λ(X,Y) := X⁴ - λX³Y - 6X²Y² + λXY³ + Y⁴, λ ∈ C[T] / {C}

denotes a family of quartic simple forms.

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