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Pseudo-elliptic integrals, units, and torsion

Francesco Pappalardi·Alfred J. van der Poorten
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Abstract

We remark on pseudo-elliptic integrals and on exceptional function fields, namely function fields defined over an infinite base field but nonetheless containing non-trivial units. Our emphasis is on some elementary criteria that must be satisfied by a squarefree polynomial whose square root generates a quadratic function field with non-trivial unit. We detail the genus 1 case.

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Francesco Pappalardi, Alfred J. van der Poorten. 2004-03-14. Pseudo-elliptic integrals, units, and torsion. https://arxiv.org/abs/math/0403228

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