Download or read book Number Theory Unit 8 Diophantine Equations written by Open University M381/Number theory/Unit 8 and published by . This book was released on 2009-05-16 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics covered in this unit include Pell's equation, The Pythagorean equation, Fermat's last Theorem, and Sums of squares.To order all 8 units in the Number Theory series please see produc M381/PP02
Download or read book Unit Equations in Diophantine Number Theory written by Jan-Hendrik Evertse and published by Cambridge University Press. This book was released on 2015-12-30 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, graduate-level treatment of unit equations and their various applications.
Download or read book Unit Equations in Diophantine Number Theory written by Jan-Hendrik Evertse and published by Cambridge University Press. This book was released on 2015-12-30 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Number Theory Diophantine and algebraic written by Kálmán Györy and published by North Holland. This book was released on 1990 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Number Theory written by Daniel Duverney and published by World Scientific Publishing Company. This book was released on 2010-09-09 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. These topics are covered in 12 chapters and more than 200 solved exercises. Clear, concise, and self-contained, this textbook may be used by undergraduate and graduate students, as well as highschool mathematics teachers. More generally, it will be suitable for all those who are interested in number theory, this fascinating branch of mathematics.
Download or read book Diophantine Equations written by and published by Academic Press. This book was released on 1969 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diophantine Equations
Download or read book An Introduction to the Theory of Numbers written by Leo Moser and published by The Trillia Group. This book was released on 2004 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers. Three sections of problems (which include exercises as well as unsolved problems) complete the text."--Publisher's description
Download or read book Arithmetic Geometry Number Theory and Computation written by Jennifer S. Balakrishnan and published by Springer Nature. This book was released on 2022-03-15 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles related to the work of the Simons Collaboration “Arithmetic Geometry, Number Theory, and Computation.” The papers present mathematical results and algorithms necessary for the development of large-scale databases like the L-functions and Modular Forms Database (LMFDB). The authors aim to develop systematic tools for analyzing Diophantine properties of curves, surfaces, and abelian varieties over number fields and finite fields. The articles also explore examples important for future research. Specific topics include● algebraic varieties over finite fields● the Chabauty-Coleman method● modular forms● rational points on curves of small genus● S-unit equations and integral points.
Download or read book Number Theory written by Kalman Gyoery and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Download or read book Number Theory written by Don Redmond and published by CRC Press. This book was released on 1996-04-23 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a detailed introduction to number theory, demonstrating how other areas of mathematics enter into the study of the properties of natural numbers. It contains problem sets within each section and at the end of each chapter to reinforce essential concepts, and includes up-to-date information on divisibility problems, polynomial congruence, the sums of squares and trigonometric sums.;Five or more copies may be ordered by college or university bookstores at a special price, available on application.
Download or read book Solving S Unit Mordell Thue Thue Mahler and Generalized Ramanujan Nagell Equations via the Shimura Taniyama Conjecture written by Rafael von Känel and published by American Mathematical Society. This book was released on 2023-06-22 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Download or read book Pell s Equation written by Edward J. Barbeau and published by Springer Science & Business Media. This book was released on 2006-05-04 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pell's equation is part of a central area of algebraic number theory that treats quadratic forms and the structure of the rings of integers in algebraic number fields. It is an ideal topic to lead college students, as well as some talented and motivated high school students, to a better appreciation of the power of mathematical technique. Even at the specific level of quadratic diophantine equations, there are unsolved problems, and the higher degree analogues of Pell's equation, particularly beyond the third, do not appear to have been well studied. In this focused exercise book, the topic is motivated and developed through sections of exercises which will allow the readers to recreate known theory and provide a focus for their algebraic practice. There are several explorations that encourage the reader to embark on their own research. A high school background in mathematics is all that is needed to get into this book, and teachers and others interested in mathematics who do not have (or have forgotten) a background in advanced mathematics may find that it is a suitable vehicle for keeping up an independent interest in the subject.
Download or read book Computational Number Theory written by Attila Pethoe and published by Walter de Gruyter. This book was released on 2011-06-01 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Diophantine Equations written by Titu Andreescu and published by Springer Science & Business Media. This book was released on 2010-09-02 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants — including Olympiad and Putnam competitors — as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.
Download or read book Classical Diophantine Equations written by Vladimir G. Sprindzuk and published by Springer. This book was released on 2006-11-15 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, now that the book appears in English, close studyand emulation. In particular those emphases allow him to devote the eighth chapter to an analysis of the interrelationship of the class number of algebraic number fields involved and the bounds on the heights of thesolutions of the diophantine equations. Those ideas warrant further development. The final chapter deals with effective aspects of the Hilbert Irreducibility Theorem, harkening back to earlier work of the author. There is no other congenial entry point to the ideas of the last two chapters in the literature.
Download or read book Diophantine Equations and Inequalities in Algebraic Number Fields written by Yuan Wang and published by Springer Science & Business Media. This book was released on 1991 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. The Circle Method and Waring's Problem.- 1.1 Introduction.- 1.2 Farey Division.- 1.3 Auxiliary Lemmas.- 1.4 Major Arcs.- 1.5 Singular Integral.- 1.6 Singular Series.- 1.7 Proof of Lemma 1.12.- 1.8 Proof of Theorem 1.1.- Notes.- 2. Complete Exponential Sums.- 2.1 Introduction.- 2.2 Several Lemmas.- 2.3 Mordell's Lemma.- 2.4 Fundamental Lemma.- 2.5 Proof of Theorem 2.1.- 2.6 Proof of Theorem 2.2.- Notes.- 3. Weyl's Sums.- 3.1 Introduction.- 3.2 Proof of Theorem 3.1.- 3.3 A Lemma on Units.- 3.4 The Asymptotic Formula for N(a, T).- 3.5 A Sum.- 3.6 Mitsui's Lemma.- 3.7 Proof of Theorem 3.3.- 3.8 Proof of Lemma 3.6.- 3.9 Continuation.- Notes.- 4. Mean Value Theorems.- 4.1 Introduction.- 4.2 Proof of Theorem 4.1.- 4.3 Proof of Theorem 4.2.- 4.4 A Lemma on the Set D.- 4.5 A Lemma on the Set D(x).- 4.6 Fundamental Lemma.- 4.7 Proof of Lemma 4.1.- Notes.- 5. The Circle Method in Algebraic Number Fields.- 5.1 Introduction.- 5.2 Lemmas.- 5.3 Asympotic Expansion forSi (?, T).- 5.4 Further Estimates on Basic Domains.- 5.5 Proof of Theorem 5.1.- 5.6 Proof of Theorem 5.2.- Notes.- 6. Singular Series and Singular Integrals.- 6.1 Introduction.- 6.2 Product Form for Singular Series.- 6.3 Singular Series and Congruences.- 6.4 p-adic Valuations.- 6.5 k-th Power Residues.- 6.6 Proof of Theorem 6.1.- 6.7 Monotonic Functions.- 6.8 Proof of Theorem 6.2.- Notes.- 7. Waring's Problem.- 7.1 Introduction.- 7.2 The Ring Jk.- 7.3 Proofs of Theorems 7.1 and 7.2.- 7.4 Proof of Theorem 7.3.- 7.5 Proof of Theorem 7.4.- Notes.- 8. Additive Equations.- 8.1 Introduction.- 8.2 Reductions.- 8.3 Contraction.- 8.4 Derived Variables.- 8.5 Proof of Theorem 8.1.- 8.6 Proof of Theorem 8.2.- 8.7 Bounds for Solutions.- Notes.- 9. Small Nonnegative Solutions of Additive Equations.- 9.1 Introduction.- 9.2 Hurwitz's Lemma.- 9.3 Reductions.- 9.4 Continuation.- 9.5 Farey Division.- 9.6 Supplementary Domain.- 9.7 Basic Domains.- 9.8 Proof of Theorem 9.1.- Notes.- 10. Small Solutions of Additive Equations.- 10.1 Introduction.- 10.2 Reductions.- 10.3 Continuation.- 10.4 Farey Division.- 10.5 Supplementary Domain.- 10.6 Basic Domains.- 10.7 Proof of Theorem 10.1.- Notes.- 11. Diophantine Inequalities for Forms.- 11.1 Introduction.- 11.2 A Single Additive Form.- 11.3 A Variant Circle Method.- 11.4 Continuation.- 11.5 Proof of Lemma 11.1.- 11.6 Linear Forms.- 11.7 A Single Form.- 11.8 Proof of Theorem 11.1.- Notes.- References I.- References II
Download or read book An Experimental Introduction to Number Theory written by Benjamin Hutz and published by American Mathematical Soc.. This book was released on 2018-04-17 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents material suitable for an undergraduate course in elementary number theory from a computational perspective. It seeks to not only introduce students to the standard topics in elementary number theory, such as prime factorization and modular arithmetic, but also to develop their ability to formulate and test precise conjectures from experimental data. Each topic is motivated by a question to be answered, followed by some experimental data, and, finally, the statement and proof of a theorem. There are numerous opportunities throughout the chapters and exercises for the students to engage in (guided) open-ended exploration. At the end of a course using this book, the students will understand how mathematics is developed from asking questions to gathering data to formulating and proving theorems. The mathematical prerequisites for this book are few. Early chapters contain topics such as integer divisibility, modular arithmetic, and applications to cryptography, while later chapters contain more specialized topics, such as Diophantine approximation, number theory of dynamical systems, and number theory with polynomials. Students of all levels will be drawn in by the patterns and relationships of number theory uncovered through data driven exploration.
