Determined sequences, continued fractions, and hyperelliptic curves

Alfred J. Van Der Poorten

Determined sequences, continued fractions, and hyperelliptic curves

Alfred J. Van Der Poorten^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

Abstract

In this report I sanitise (in the sense of 'bring some sanity to') the arguments of earlier reports detailing the correspondence between sequences (M + hS)_-∞<h<∞ of divisors on elliptic and genus two hyperelliptic curves, the continued fraction expansion of quadratic irrational functions in the relevant elliptic and hyperelliptic function fields, and certain integer sequences satisfying relations of Somos type. I note that one may often readily determine the coefficients in those relations by elementary linear algebra.

Original language	English
Title of host publication	Algorithmic Number Theory - 7th International Symposium, ANTS-VII, Proceedings
Editors	Florian Hess, Sebastian Pauli, Michael Pohst
Publisher	Springer, Springer Nature
Pages	393-405
Number of pages	13
Volume	4076 LNCS
ISBN (Print)	3540360751, 9783540360759
Publication status	Published - 2006
Event	7th International Symposium on Algorithmic Number Theory, ANTS-VII - Berlin, Germany Duration: 23 Jul 2006 → 28 Jul 2006

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4076 LNCS
ISSN (Print)	03029743
ISSN (Electronic)	16113349

Other

Other	7th International Symposium on Algorithmic Number Theory, ANTS-VII
Country/Territory	Germany
City	Berlin
Period	23/07/06 → 28/07/06

Cite this

Van Der Poorten, A. J. (2006). Determined sequences, continued fractions, and hyperelliptic curves. In F. Hess, S. Pauli, & M. Pohst (Eds.), Algorithmic Number Theory - 7th International Symposium, ANTS-VII, Proceedings (Vol. 4076 LNCS, pp. 393-405). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4076 LNCS). Springer, Springer Nature.

Van Der Poorten, Alfred J. / Determined sequences, continued fractions, and hyperelliptic curves. Algorithmic Number Theory - 7th International Symposium, ANTS-VII, Proceedings. editor / Florian Hess ; Sebastian Pauli ; Michael Pohst. Vol. 4076 LNCS Springer, Springer Nature, 2006. pp. 393-405 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Determined sequences, continued fractions, and hyperelliptic curves",

abstract = "In this report I sanitise (in the sense of 'bring some sanity to') the arguments of earlier reports detailing the correspondence between sequences (M + hS)-∞ of divisors on elliptic and genus two hyperelliptic curves, the continued fraction expansion of quadratic irrational functions in the relevant elliptic and hyperelliptic function fields, and certain integer sequences satisfying relations of Somos type. I note that one may often readily determine the coefficients in those relations by elementary linear algebra.",

author = "{Van Der Poorten}, {Alfred J.}",

year = "2006",

language = "English",

isbn = "3540360751",

volume = "4076 LNCS",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer, Springer Nature",

pages = "393--405",

editor = "Florian Hess and Sebastian Pauli and Michael Pohst",

booktitle = "Algorithmic Number Theory - 7th International Symposium, ANTS-VII, Proceedings",

address = "United States",

note = "7th International Symposium on Algorithmic Number Theory, ANTS-VII ; Conference date: 23-07-2006 Through 28-07-2006",

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Van Der Poorten, AJ 2006, Determined sequences, continued fractions, and hyperelliptic curves. in F Hess, S Pauli & M Pohst (eds), Algorithmic Number Theory - 7th International Symposium, ANTS-VII, Proceedings. vol. 4076 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4076 LNCS, Springer, Springer Nature, pp. 393-405, 7th International Symposium on Algorithmic Number Theory, ANTS-VII, Berlin, Germany, 23/07/06.

Determined sequences, continued fractions, and hyperelliptic curves. / Van Der Poorten, Alfred J.

Algorithmic Number Theory - 7th International Symposium, ANTS-VII, Proceedings. ed. / Florian Hess; Sebastian Pauli; Michael Pohst. Vol. 4076 LNCS Springer, Springer Nature, 2006. p. 393-405 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4076 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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AB - In this report I sanitise (in the sense of 'bring some sanity to') the arguments of earlier reports detailing the correspondence between sequences (M + hS)-∞ of divisors on elliptic and genus two hyperelliptic curves, the continued fraction expansion of quadratic irrational functions in the relevant elliptic and hyperelliptic function fields, and certain integer sequences satisfying relations of Somos type. I note that one may often readily determine the coefficients in those relations by elementary linear algebra.

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VL - 4076 LNCS

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Van Der Poorten AJ. Determined sequences, continued fractions, and hyperelliptic curves. In Hess F, Pauli S, Pohst M, editors, Algorithmic Number Theory - 7th International Symposium, ANTS-VII, Proceedings. Vol. 4076 LNCS. Springer, Springer Nature. 2006. p. 393-405. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

Determined sequences, continued fractions, and hyperelliptic curves

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