Torsion points, Pell’s equation, and integration in elementary terms
Torsion points, Pell’s equation, and integration in elementary terms
The main results of this paper involve general algebraic differentials $\omega$ on a general pencil of algebraic curves. We show how to determine if $\omega$ is integrable in elementary terms for infinitely many members of the pencil. In particular, this corrects an assertion of James Davenport from 1981 and provides …