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Author : Andrej Dujella
Publisher : Springer Nature
ISBN 13 : 3031567242
Total Pages : 343 pages
Book Rating : 4.0/5 (315 download)
Download or read book Diophantine m-tuples and Elliptic Curves written by Andrej Dujella and published by Springer Nature. This book was released on with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Andrej Dujella
Publisher : Springer
ISBN 13 : 9783031567230
Total Pages : 0 pages
Book Rating : 4.5/5 (672 download)
Download or read book Diophantine m-tuples and Elliptic Curves written by Andrej Dujella and published by Springer. This book was released on 2024-05-19 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Richard Guy
Publisher : Springer Science & Business Media
ISBN 13 : 0387266771
Total Pages : 455 pages
Book Rating : 4.3/5 (872 download)
Download or read book Unsolved Problems in Number Theory written by Richard Guy and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloane’s Online Encyclopedia of Integer Sequences, at the end of several of the sections.
Author :
Publisher :
ISBN 13 :
Total Pages : 260 pages
Book Rating : 4.:/5 (318 download)
Download or read book Proceedings of the Japan Academy written by and published by . This book was released on 2000 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Trygve Nagell
Publisher : American Mathematical Soc.
ISBN 13 : 1470463245
Total Pages : 309 pages
Book Rating : 4.4/5 (74 download)
Download or read book Introduction to Number Theory written by Trygve Nagell and published by American Mathematical Soc.. This book was released on 2021-07-21 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author :
Publisher :
ISBN 13 :
Total Pages : 460 pages
Book Rating : 4.8/5 (157 download)
Download or read book Glasnik Matematički written by and published by . This book was released on 2007 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Joseph H. Silverman
Publisher : Springer Science & Business Media
ISBN 13 : 1475742525
Total Pages : 292 pages
Book Rating : 4.4/5 (757 download)
Download or read book Rational Points on Elliptic Curves written by Joseph H. Silverman and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book’s accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.
Author : Andrej Dujella
Publisher :
ISBN 13 : 9789530308978
Total Pages : 636 pages
Book Rating : 4.3/5 (89 download)
Download or read book Number Theory written by Andrej Dujella and published by . This book was released on 2021 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. E. Cremona
Publisher : CUP Archive
ISBN 13 : 9780521598200
Total Pages : 388 pages
Book Rating : 4.5/5 (982 download)
Download or read book Algorithms for Modular Elliptic Curves Full Canadian Binding written by J. E. Cremona and published by CUP Archive. This book was released on 1997-05-15 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an extensive set of tables giving information about elliptic curves.
Author : Henri Darmon
Publisher : American Mathematical Soc.
ISBN 13 : 0821828681
Total Pages : 146 pages
Book Rating : 4.8/5 (218 download)
Download or read book Rational Points on Modular Elliptic Curves written by Henri Darmon and published by American Mathematical Soc.. This book was released on 2004 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book surveys some recent developments in the arithmetic of modular elliptic curves. It places a special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modularity in shedding light on these two closely related issues. The main theme of the book is the theory of complex multiplication, Heegner points, and some conjectural variants. The first three chapters introduce the background and prerequisites: elliptic curves, modular forms and the Shimura-Taniyama-Weil conjecture, complex multiplication and the Heegner point construction. The next three chapters introduce variants of modular parametrizations in which modular curves are replaced by Shimura curves attached to certain indefinite quaternion algebras. The main new contributions are found in Chapters 7-9, which survey the author's attempts to extend the theory of Heegner points and complex multiplication to situations where the base field is not a CM field. Chapter 10 explains the proof of Kolyvagin's theorem, which relates Heegner points to the arithmetic of elliptic curves and leads to the best evidence so far for the Birch and Swinnerton-Dyer conjecture.
Author :
Publisher :
ISBN 13 :
Total Pages : 694 pages
Book Rating : 4.3/5 (91 download)
Download or read book Journal de théorie des nombres de Bordeaux written by and published by . This book was released on 2001 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 872 pages
Book Rating : 4.3/5 (91 download)
Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 872 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Władysław Narkiewicz
Publisher : Springer Science & Business Media
ISBN 13 : 0857295322
Total Pages : 659 pages
Book Rating : 4.8/5 (572 download)
Download or read book Rational Number Theory in the 20th Century written by Władysław Narkiewicz and published by Springer Science & Business Media. This book was released on 2011-09-02 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat’s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area.
Author : Richard Guy
Publisher : Springer Science & Business Media
ISBN 13 : 1475717385
Total Pages : 176 pages
Book Rating : 4.4/5 (757 download)
Download or read book Unsolved Problems in Number Theory written by Richard Guy and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second edition sold 2241 copies in N.A. and 1600 ROW. New edition contains 50 percent new material.
Author : Joseph H. Silverman
Publisher : Springer Science & Business Media
ISBN 13 : 1475719205
Total Pages : 414 pages
Book Rating : 4.4/5 (757 download)
Download or read book The Arithmetic of Elliptic Curves written by Joseph H. Silverman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.
Author : Ian Stewart
Publisher : CRC Press
ISBN 13 : 143986408X
Total Pages : 334 pages
Book Rating : 4.4/5 (398 download)
Download or read book Algebraic Number Theory and Fermat's Last Theorem written by Ian Stewart and published by CRC Press. This book was released on 2001-12-12 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a completely revised third edition. It reflects the exciting developments in number theory during the past two decades that culminated in the proof of Fermat's Last Theorem. Intended as a upper level textbook, it
Author : M. Hazewinkel
Publisher : Springer
ISBN 13 : 1489937951
Total Pages : 967 pages
Book Rating : 4.4/5 (899 download)
Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-12-01 with total page 967 pages. Available in PDF, EPUB and Kindle. Book excerpt:
