J. Aust. Math. Soc.  79 (2005), 335-347
Pseudo-elliptic integrals, units, and torsion

Francesco Pappalardi
  Dipartimento di Matematica
  Universit\`a degli Studi Roma Tre
  L.go San Leonardo Murialdo, 1
  I-00146 Roma
  Italy
  pappa@mat.uniroma3.it
and
Alfred J. van der Poorten
  Centre for Number Theory Research
  1 Bimbil Place, Killara
  Sydney NSW 2071
  Australia
  alf@math.mq.edu.au


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.
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