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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 : Serge Lang
Publisher : Springer
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.3/5 (91 download)
Download or read book Elliptic Curves written by Serge Lang and published by Springer. This book was released on 1978 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 :
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 : 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 : 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 : Joseph H. Silverman
Publisher : Springer Science & Business Media
ISBN 13 : 9780387978253
Total Pages : 300 pages
Book Rating : 4.9/5 (782 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 1994-11-18 with total page 300 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 : 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 :
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (141 download)
Download or read book Elliptic Curves written by and published by . This book was released on 1973 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : S. Lang
Publisher :
ISBN 13 : 9783662070116
Total Pages : 280 pages
Book Rating : 4.0/5 (71 download)
Download or read book Elliptic Curves written by S. Lang and published by . This book was released on 2014-01-15 with total page 280 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 : 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:
Author : Susanne Schmitt
Publisher : Walter de Gruyter
ISBN 13 : 3110198010
Total Pages : 378 pages
Book Rating : 4.1/5 (11 download)
Download or read book Elliptic Curves written by Susanne Schmitt and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: The basics of the theory of elliptic curves should be known to everybody, be he (or she) a mathematician or a computer scientist. Especially everybody concerned with cryptography should know the elements of this theory. The purpose of the present textbook is to give an elementary introduction to elliptic curves. Since this branch of number theory is particularly accessible to computer-assisted calculations, the authors make use of it by approaching the theory under a computational point of view. Specifically, the computer-algebra package SIMATH can be applied on several occasions. However, the book can be read also by those not interested in any computations. Of course, the theory of elliptic curves is very comprehensive and becomes correspondingly sophisticated. That is why the authors made a choice of the topics treated. Topics covered include the determination of torsion groups, computations regarding the Mordell-Weil group, height calculations, S-integral points. The contents is kept as elementary as possible. In this way it becomes obvious in which respect the book differs from the numerous textbooks on elliptic curves nowadays available.
