Diophantine M Tuples And Elliptic Curves

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Diophantine M Tuples And Elliptic Curves

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Author : Andrej Dujella
language : en
Publisher: Springer
Release Date : 2024-05-19

Diophantine M Tuples And Elliptic Curves written by Andrej Dujella and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-19 with Mathematics categories.

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.

Diophantine M Tuples And Elliptic Curves

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Author : Andrej Dujella
language : en
Publisher: Springer Nature
Release Date : 2024-06-05

Diophantine M Tuples And Elliptic Curves written by Andrej Dujella and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-05 with Mathematics categories.

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.

Class Groups Of Number Fields And Related Topics

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Author : Kalyan Chakraborty
language : en
Publisher: Springer Nature
Release Date : 2024-12-02

Class Groups Of Number Fields And Related Topics written by Kalyan Chakraborty and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-02 with Mathematics categories.

This book collects original research papers and survey articles presented at two conferences on the same theme: the International Conference on Class Groups of Number Fields and Related Topics, held at Kerala School of Mathematics, Kozhikode, Kerala, India, from 21–24 October 2021 and then from 21–24 November 2022. It presents the fundamental research problems that arise in the study of class groups of number fields and related areas. The book also covers some new techniques and tools to study these problems. Topics in this book include class groups of number fields, units, Ankeny–Artin–Chowla conjecture, Iwasawa theory, elliptic curves, Diophantine equations, partition functions, Diophantine tuples, congruent numbers, Carmichael ideals in a number field and their connection with class groups. This book will be a valuable resource for graduate students and researchers in mathematics interested in class groups of number fields and their connections to other branches of mathematics. It also attracts new researchers to the field and young researchers will benefit immensely from the diverse problems discussed in this book. All the contributing authors are leading academicians, scientists and profound researchers. This book is dedicated to Prof. Michel Waldschmidt, a renowned French number theorist, on his 75th birthday.

Unsolved Problems In Number Theory

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Author : Richard Guy
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Unsolved Problems In Number Theory written by Richard Guy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

Mathematics is kept alive by the appearance of new unsolved problems, problems posed from within mathematics itself, and also from the increasing number of disciplines where mathematics is applied. This book provides a steady supply of easily understood, if not easily solved, problems which can be considered in varying depths by mathematicians at all levels of mathematical maturity. For this new edition, the author has included new problems on symmetric and asymmetric primes, sums of higher powers, Diophantine m-tuples, and Conway's RATS and palindromes. The author has also included a useful new feature at the end of several of the sections: lists of references to OEIS, Neil Sloane's Online Encyclopedia of Integer Sequences. About the first Edition: "...many talented young mathematicians will write their first papers starting out from problems found in this book." András Sárközi, MathSciNet

The Enchantment Of Numbers

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Author : Eric L. F. Roettger
language : en
Publisher: Springer Nature
Release Date : 2025-07-01

The Enchantment Of Numbers written by Eric L. F. Roettger and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-01 with Mathematics categories.

Inspired by the classic Recreations in the Theory of Numbers—The Queen of Mathematics Entertains by Albert H. Beiler, this book brings the excitement of recreational number theory into the 21st century through the lens of computational techniques. While Beiler’s work, originally published in 1964, captivated readers with its breadth and charm, some sections have become dated. Here, we re-examine most of the key topics Beiler covered, while introducing fresh updates and insights rooted in computational number theory. The authors aim to present efficient computer algorithms to tackle various problems that arise in the theory of numbers, providing a deeper and more modern perspective on these timeless puzzles. Though we cannot rival Beiler’s exuberant prose, we hope our enduring fascination with these topics — cultivated over decades of study and teaching — will shine through and resonate with readers. The book is structured into 21 chapters, each focusing on different facets of number theory with which the authors have extensive expertise. From ancient problems to contemporary computational challenges, this volume will reignite the joy and wonder found in numbers while incorporating the power of modern computation. Whether you're a seasoned mathematician or a curious learner, this book promises a journey through the rich and playful landscape of number theory, making both historical and new discoveries accessible to all.

Proceedings Of The Japan Academy

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Author :
language : en
Publisher:
Release Date : 2000

Proceedings Of The Japan Academy written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

Glasnik Matemati Ki

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Author :
language : en
Publisher:
Release Date : 2007

Glasnik Matemati Ki written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

Number Theory

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Author : Andrej Dujella
language : en
Publisher:
Release Date : 2021

Number Theory written by Andrej Dujella and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.

Introduction To Number Theory

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Author : Trygve Nagell
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-07-21

Introduction To Number Theory written by Trygve Nagell and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-21 with Education categories.

A special feature of Nagell's well-known text is the rather extensive treatment of Diophantine equations of second and higher degree. A large number of non-routine problems are given. Reviews & Endorsements This is a very readable introduction to number theory, with particular emphasis on diophantine equations, and requires only a school knowledge of mathematics. The exposition is admirably clear. More advanced or recent work is cited as background, where relevant … [T]here are welcome novelties: Gauss's own evaluation of Gauss's sums, which is still perhaps the most elegant, is reproduced apparently for the first time. There are 180 examples, many of considerable interest, some of these being little known. -- Mathematical Reviews

Journal De Th Orie Des Nombres De Bordeaux

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Author :
language : en
Publisher:
Release Date : 2001

Journal De Th Orie Des Nombres De Bordeaux written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Number theory categories.