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Pseudo-elliptic integrals, units, and torsion

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  09 April 2009

Francesco Pappalardi  and
Alfred J. Van Der Poorten
Francesco Pappalardi
Affiliation:
Dipartimento di Matematica, Università degli Studi Roma Tre, L.go San Lenardo Murialdo, 1, I-00146 Roma, Italy, e-mail: [email protected]
Alfred J. Van Der Poorten
Affiliation:
Centre for Number Theory Research, 1 Bimbil Place, Killara, Sydney NSW 2071, Australia, e-mail: [email protected]
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Abstract

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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 I case.

Keywords

quadratic function field of characteristic zero.

MSC classification

Secondary: 11J70: Continued fractions and generalizations 11J68: Approximation to algebraic numbers
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 79 , Issue 3 , December 2005 , pp. 335 - 347
Copyright
Copyright © Australian Mathematical Society 2005

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