TY - JOUR
T1 - Pseudo-elliptic integrals, units, and torsion
AU - Pappalardi, Francesco
AU - Van Der Poorten, Alfred J.
PY - 2005/12
Y1 - 2005/12
N2 - 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.
AB - 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.
KW - Quadratic function field of characteristic zero
UR - http://www.scopus.com/inward/record.url?scp=31144458339&partnerID=8YFLogxK
U2 - 10.1017/S1446788700010934
DO - 10.1017/S1446788700010934
M3 - Article
AN - SCOPUS:31144458339
SN - 1446-7887
VL - 79
SP - 335
EP - 347
JO - Journal of the Australian Mathematical Society
JF - Journal of the Australian Mathematical Society
IS - 3
ER -