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| Author | : Peter B. Borwein |
| Publisher | : |
| Total Pages | : 220 |
| Release | : 2002 |
| Genre | : Diophantine analysis |
| ISBN | : |
| Author | : Peter Borwein |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 220 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 0387216529 |
This introduction to computational number theory is centered on a number of problems that live at the interface of analytic, computational and Diophantine number theory, and provides a diverse collection of techniques for solving number- theoretic problems. There are many exercises and open research problems included.
| Author | : Charles Stanley Ogilvy |
| Publisher | : Courier Corporation |
| Total Pages | : 196 |
| Release | : 1988-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780486257785 |
Challenging, accessible mathematical adventures involving prime numbers, number patterns, irrationals and iterations, calculating prodigies, and more. No special training is needed, just high school mathematics and an inquisitive mind. "A splendidly written, well selected and presented collection. I recommend the book unreservedly to all readers." — Martin Gardner.
| Author | : Ilker Inam |
| Publisher | : Springer |
| Total Pages | : 363 |
| Release | : 2019-04-17 |
| Genre | : Mathematics |
| ISBN | : 3030125580 |
This volume collects lecture notes and research articles from the International Autumn School on Computational Number Theory, which was held at the Izmir Institute of Technology from October 30th to November 3rd, 2017 in Izmir, Turkey. Written by experts in computational number theory, the chapters cover a variety of the most important aspects of the field. By including timely research and survey articles, the text also helps pave a path to future advancements. Topics include: Modular forms L-functions The modular symbols algorithm Diophantine equations Nullstellensatz Eisenstein series Notes from the International Autumn School on Computational Number Theory will offer graduate students an invaluable introduction to computational number theory. In addition, it provides the state-of-the-art of the field, and will thus be of interest to researchers interested in the field as well.
| Author | : Istvan Gaal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 192 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461200857 |
Work examines the latest algorithms and tools to solve classical types of diophantine equations.; Unique book---closest competitor, Smart, Cambridge, does not treat index form equations.; Author is a leading researcher in the field of computational algebraic number theory.; The text is illustrated with several tables of various number fields, including their data on power integral bases.; Several interesting properties of number fields are examined.; Some infinite parametric families of fields are also considered as well as the resolution of the corresponding infinite parametric families of diophantine equations.
| Author | : Jan-Hendrik Evertse |
| Publisher | : Cambridge University Press |
| Total Pages | : 381 |
| Release | : 2015-12-30 |
| Genre | : Mathematics |
| ISBN | : 1316432351 |
Diophantine number theory is an active area that has seen tremendous growth over the past century, and in this theory unit equations play a central role. This comprehensive treatment is the first volume devoted to these equations. The authors gather together all the most important results and look at many different aspects, including effective results on unit equations over number fields, estimates on the number of solutions, analogues for function fields and effective results for unit equations over finitely generated domains. They also present a variety of applications. Introductory chapters provide the necessary background in algebraic number theory and function field theory, as well as an account of the required tools from Diophantine approximation and transcendence theory. This makes the book suitable for young researchers as well as experts who are looking for an up-to-date overview of the field.
| Author | : Attila Pethoe |
| Publisher | : Walter de Gruyter |
| Total Pages | : 357 |
| Release | : 2011-06-01 |
| Genre | : Mathematics |
| ISBN | : 3110865955 |
| Author | : Daniel Duverney |
| Publisher | : World Scientific |
| Total Pages | : 348 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 9814307467 |
This textbook presents an elementary introduction to number theory and its different aspects: approximation of real numbers, irrationality and transcendence problems, continued fractions, diophantine equations, quadratic forms, arithmetical functions and algebraic number theory. Clear, concise, and self-contained, the topics are covered in 12 chapters with more than 200 solved exercises. The textbook may be used by undergraduates and graduate students, as well as high school mathematics teachers. More generally, it will be suitable for all those who are interested in number theory, the fascinating branch of mathematics.
| Author | : H. G. Zimmer |
| Publisher | : Springer |
| Total Pages | : 108 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540374663 |
| Author | : Jorn Steuding |
| Publisher | : CRC Press |
| Total Pages | : 275 |
| Release | : 2005-05-19 |
| Genre | : Mathematics |
| ISBN | : 1584884827 |
While its roots reach back to the third century, diophantine analysis continues to be an extremely active and powerful area of number theory. Many diophantine problems have simple formulations, they can be extremely difficult to attack, and many open problems and conjectures remain. Diophantine Analysis examines the theory of diophantine approximations and the theory of diophantine equations, with emphasis on interactions between these subjects. Beginning with the basic principles, the author develops his treatment around the theory of continued fractions and examines the classic theory, including some of its applications. He also explores modern topics rarely addressed in other texts, including the abc conjecture, the polynomial Pell equation, and the irrationality of the zeta function and touches on topics and applications related to discrete mathematics, such as factoring methods for large integers. Setting the stage for tackling the field's many open problems and conjectures, Diophantine Analysis is an ideal introduction to the fundamentals of this venerable but still dynamic field. A detailed appendix supplies the necessary background material, more than 200 exercises reinforce the concepts, and engaging historical notes bring the subject to life.
