On the Interpretations of the History of Diophantine Analysis: A Comparative Study of Alternate Perspectives

Ganita Bharati 40 (3):115-152 (2018)
  Copy   BIBTEX

Abstract

Essay Review of “Les Arithmétiques de Diophante. Lecture historique et mathématique” by Roshdi Rashed and Christian Houzel, and Histoire de l’analyse diophantienne classique : d’Abū Kamil à Fermat by Roshdi Rashed.

Categories

Keywords

Reprint years

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,202

External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Classification of Quantifier Prefixes Over Diophantine Equations.Some Diophantine Forms of Godel's Theorem.Universal Diophantine Equation.Exponential Diophantine Representation of Recursively Enumerable Sets.Register Machine Proof of the Theorem on Exponential Diophantine Representation of Enumerable Sets.James P. Jones, Verena H. Dyson, John C. Shepherdson & J. P. Jones - 1986 - Journal of Symbolic Logic 51 (2):477-479.
Diophantine equivalence and countable rings.Alexandra Shlapentokh - 1994 - Journal of Symbolic Logic 59 (3):1068-1095.
Division by zero.Emil Jeřábek - 2016 - Archive for Mathematical Logic 55 (7-8):997-1013.
Diophantine properties of finite commutative rings.Mihai Prunescu - 2003 - Archive for Mathematical Logic 42 (3):293-302.
History of the Theory of Numbers: Vol. II "Diophantine Analysis" by L. E. Dickson. [REVIEW]J. Child - 1921 - Isis 4:107-108.
Diophantine Induction.Richard Kaye - 1990 - Annals of Pure and Applied Logic 46 (1):1-40.
On the youthful writings of Louis J. Mordell on the Diophantine equation y2-k=x3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y^2-k=x^3$$\end{document}. [REVIEW]François Lê & Sébastien Gauthier - 2019 - Archive for History of Exact Sciences 73 (5):427-468.
The exponential diophantine problem for.Mihai Prunescu - 2020 - Journal of Symbolic Logic 85 (2):671-672.
On the existence of a new family of diophantine equations for Ω.Toby Ord - 2003 - Fundamenta Informaticae 56:273-284.
Review: James Ax, Simon Kochen, Diophantine Problems Over Local Fields I; James Ax, Simon Kochen, Diophantine Problems Over Local Fields II. A Complete set of Axioms for $p$-adic number theory; James Ax, Simon Kochen, Diophantine Problems over Local Field III. Decidable Fields. [REVIEW]Abraham Robinson - 1971 - Journal of Symbolic Logic 36 (4):683-684.
Diophantine definability over non-finitely generated non-degenerate modules of algebraic extensions of ℚ.Alexandra Shlapentokh - 2001 - Archive for Mathematical Logic 40 (4):297-328.
Note on Quantifier Prefixes Over Diophantine Equations.Classification of Quantifier Prefixes over Exponential Diophantine Equations.Shih Ping Tung - 1988 - Journal of Symbolic Logic 53 (1):309-310.
Review: Charles N. Delzell, Note on Quantifier Prefixes Over Diophantine Equations; J. P. Jones, H. Levitz, A. J. Wilkie, Classification of Quantifier Prefixes over Exponential Diophantine Equations. [REVIEW]Shih Ping Tung - 1988 - Journal of Symbolic Logic 53 (1):309-310.
Existential arithmetization of Diophantine equations.Yuri Matiyasevich - 2009 - Annals of Pure and Applied Logic 157 (2-3):225-233.
Verena H. Dyson, James P. Jones, and John C. Shepherdson. Some diophantine forms of Gödel's theorem. Archiv für mathematische Logik und Grundlagenforschung, vol. 22 , pp. 51–60. - James P. Jones. Universal diophantine equation. The journal of symbolic logic, vol. 47 , pp. 549–571. - J. P. Jones and Ju. V. Matijasevič. Exponential diophantine representation of recursively enumerable sets. English with French abstract. Proceedings of the Herbrand Symposium, Logic Colloquium '81, Proceedings of the Herbrand Symposium held in Marseilles, France, July 1981, edited by J. Stern, Studies in logic and the foundations of mathematics, vol. 107, North-Holland Publishing Company, Amsterdam, New York, and Oxford, 1982, pp. 159–177. - J. P. Jones and Y. V. Matijasevič. Register machine proof of the theorem on exponential diophantine representation of enumerable sets. The journal of symbolic logic, vol. 49 , pp. 818–829. [REVIEW]Martin Davis - 1986 - Journal of Symbolic Logic 51 (2):477-479.

Analytics

Added to PP
2023-05-30

Downloads
0

6 months
0

Historical graph of downloads

Sorry, there are not enough data points to plot this chart.
How can I increase my downloads?

Author's Profile

Ioannis Vandoulakis
Open University of Cyprus

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references