Pseudo-elliptic integrals, units, and torsion

Francesco Pappalardi; Alfred J. Van Der Poorten

doi:10.1017/S1446788700010934

Pseudo-elliptic integrals, units, and torsion

Francesco Pappalardi, Alfred J. Van Der Poorten^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	335-347
Number of pages	13
Journal	Journal of the Australian Mathematical Society
Volume	79
Issue number	3
DOIs	https://doi.org/10.1017/S1446788700010934
Publication status	Published - Dec 2005

Keywords

Quadratic function field of characteristic zero

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10.1017/S1446788700010934

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title = "Pseudo-elliptic integrals, units, and torsion",

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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AU - Van Der Poorten, Alfred J.

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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

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DO - 10.1017/S1446788700010934

M3 - Article

AN - SCOPUS:31144458339

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SP - 335

EP - 347

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

IS - 3

ER -

Pseudo-elliptic integrals, units, and torsion

Abstract

Keywords

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