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Diophantine m-tuples and Elliptic Curves

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Diophantine m-tuples and Elliptic Curves
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Knyga kietu viršeliu 220,20 €
2025-07-31 220.2000 InStock
Nemokamas pristatymas į paštomatus per 18-22 darbo dienų užsakymams nuo 19,00 €

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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.

Informacija

Autorius: Andrej Dujella
Serija: Developments in Mathematics
Leidėjas: Springer Nature Switzerland
Išleidimo metai: 2024
Knygos puslapių skaičius: 348
ISBN-10: 3031567234
ISBN-13: 9783031567230
Formatas: Knyga kietu viršeliu
Kalba: Anglų
Žanras: Number theory

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