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 $D(x)$ whose square root generates a quadratic function field with non-trivial unit. We detail the genus 1 case.
Pappalardi, F., VAN DER POORTEN, A.J. (2005). Pseudo-elliptic integrals, units, and torsion. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 79(3), 335-347.
Pseudo-elliptic integrals, units, and torsion
PAPPALARDI, FRANCESCO;
2005-01-01
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 $D(x)$ whose square root generates a quadratic function field with non-trivial unit. We detail the genus 1 case.File in questo prodotto:
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