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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Arithmetik & Algebra Diophantine m-tuples and Elliptic Curves
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Diophantine m-tuples and Elliptic Curves
Andrej Dujella (Broschiert, Englisch)
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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. 139,09 €
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Technische Daten
Erscheinungsdatum
06.06.2025
Sprache
Englisch
EAN
9783031567261
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Developments in Mathematics
Sonderedition
Nein
Autor
Andrej Dujella
Seitenanzahl
335
Einbandart
Broschiert
Schlagwörter
Diophantine Equations, Diophantine Quadruples, Elliptic Curves, Torsion Group, Rank of Elliptic Curves, Applications of Linear Forms in Logarithms, Integer Points on Elliptic Curves, History of Number Theory, Open Problems in Number Theory
Thema-Inhalt
PBH - Zahlentheorie
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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