Diophantine m-tuples and Elliptic Curves

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Beschreibung

This book provides an overview of the main results and problems concerning Diophantine m-tuples, i.e., sets of integers or rationals with the property that the product of any two of them is one less than a square, and their connections with elliptic curves. It presents the contributions of famous mathematicians of the past, like Diophantus, Fermat and Euler, as well as some recent results of the author and his collaborators.

The book presents fragments of the history of Diophantine m-tuples, emphasising the connections between Diophantine m-tuples and elliptic curves. It is shown how elliptic curves are used in solving some longstanding problems on Diophantine m-tuples, such as the existence of infinite families of rational Diophantine sextuples. On the other hand, rational Diophantine m-tuples are used to construct elliptic curves with interesting Mordell¿Weil groups, including curves of record rank with agiven torsion group. The book contains concrete algorithms and advice on how to use the software package PARI/GP for solving computational problems.

This book is primarily intended for researchers and graduate students in Diophantine equations and elliptic curves. However, it can be of interest to other mathematicians interested in number theory and arithmetic geometry. The prerequisites are on the level of a standard first course in elementary number theory. Background in elliptic curves, Diophantine equations and Diophantine approximations is provided.

Über den Autor

Andrej Dujella is a professor of mathematics at the University of Zagreb, Fellow of the Croatian Academy of Sciences and Arts and Doctor Honoris Causa of University of Debrecen. His research interests include Diophantine equations, elliptic curves, polynomial root separation, and applications of Diophantine approximation to cryptography.

Inhaltsverzeichnis

Introduction.- Elliptic curves over the rationals.- Elliptic curves induced by Diophantine triples.- Integer points on elliptic curves.- Sets with the property D(n).

Details

Erscheinungsjahr:	2024
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Developments in Mathematics
Inhalt:	xi 335 S. 7 s/w Illustr. 335 p. 7 illus.
ISBN-13:	9783031567230
ISBN-10:	3031567234
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Dujella, Andrej
Hersteller:	Springer Nature Switzerland Springer International Publishing AG Developments in Mathematics
Maße:	241 x 160 x 25 mm
Von/Mit:	Andrej Dujella
Erscheinungsdatum:	05.06.2024
Gewicht:	0,688 kg

Artikel-ID: 128637112

Über den Autor

Inhaltsverzeichnis

Introduction.- Elliptic curves over the rationals.- Elliptic curves induced by Diophantine triples.- Integer points on elliptic curves.- Sets with the property D(n).

Details

Erscheinungsjahr:	2024
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Developments in Mathematics
Inhalt:	xi 335 S. 7 s/w Illustr. 335 p. 7 illus.
ISBN-13:	9783031567230
ISBN-10:	3031567234
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Dujella, Andrej
Hersteller:	Springer Nature Switzerland Springer International Publishing AG Developments in Mathematics
Maße:	241 x 160 x 25 mm
Von/Mit:	Andrej Dujella
Erscheinungsdatum:	05.06.2024
Gewicht:	0,688 kg