Download or read book Auxiliary Polynomials in Number Theory written by David Masser and published by Cambridge University Press. This book was released on 2016-07-21 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unified account of various aspects of a powerful classical method, easy to understand in its simplest forms, is illustrated by applications in several areas of number theory. As well as including diophantine approximation and transcendence, which were mainly responsible for its invention, the author places the method in a broader context by exploring its application in other areas, such as exponential sums and counting problems in both finite fields and the field of rationals. Throughout the book, the method is explained in a 'molecular' fashion, where key ideas are introduced independently. Each application is the most elementary significant example of its kind and appears with detailed references to subsequent developments, making it accessible to advanced undergraduates as well as postgraduate students in number theory or related areas. It provides over 700 exercises both guiding and challenging, while the broad array of applications should interest professionals in fields from number theory to algebraic geometry.
Download or read book Auxiliary Polynomials in Number Theory written by David William Masser and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified account of a powerful classical method, illustrated by applications in number theory. Aimed at graduates and professionals.
Download or read book Number Theory and Polynomials written by James Fraser McKee and published by Cambridge University Press. This book was released on 2008-05-08 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributions by leading experts in the field provide a snapshot of current progress in polynomials and number theory.
Download or read book Additive Number Theory of Polynomials Over a Finite Field written by Gove W. Effinger and published by . This book was released on 1991 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book helps gather the sum of additive number theory.
Download or read book Transcendental Number Theory written by Alan Baker and published by Cambridge University Press. This book was released on 2022-06-09 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Alan Baker's systematic account of transcendental number theory, with a new introduction and afterword explaining recent developments.
Download or read book A Brief Guide to Algebraic Number Theory written by H. P. F. Swinnerton-Dyer and published by Cambridge University Press. This book was released on 2001-02-22 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Download or read book Analytic Number Theory written by Yoichi Motohashi and published by Cambridge University Press. This book was released on 1997-10-16 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authoritative, up-to-date review of analytic number theory containing outstanding contributions from leading international figures.
Download or read book Analytic Number Theory written by B. Berndt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: On April 25-27, 1989, over a hundred mathematicians, including eleven from abroad, gathered at the University of Illinois Conference Center at Allerton Park for a major conference on analytic number theory. The occa sion marked the seventieth birthday and impending (official) retirement of Paul T. Bateman, a prominent number theorist and member of the mathe matics faculty at the University of Illinois for almost forty years. For fifteen of these years, he served as head of the mathematics department. The conference featured a total of fifty-four talks, including ten in vited lectures by H. Delange, P. Erdos, H. Iwaniec, M. Knopp, M. Mendes France, H. L. Montgomery, C. Pomerance, W. Schmidt, H. Stark, and R. C. Vaughan. This volume represents the contents of thirty of these talks as well as two further contributions. The papers span a wide range of topics in number theory, with a majority in analytic number theory.
Download or read book Polynomial Methods in Combinatorics written by Larry Guth and published by American Mathematical Soc.. This book was released on 2016-06-10 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields, which was considered a deep and difficult problem in combinatorial geometry. The author also discusses in detail various problems in incidence geometry associated to Paul Erdős's famous distinct distances problem in the plane from the 1940s. The proof techniques are also connected to error-correcting codes, Fourier analysis, number theory, and differential geometry. Although the mathematics discussed in the book is deep and far-reaching, it should be accessible to first- and second-year graduate students and advanced undergraduates. The book contains approximately 100 exercises that further the reader's understanding of the main themes of the book.
Download or read book Around the Unit Circle written by James McKee and published by Springer Nature. This book was released on 2021-12-08 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mahler measure, a height function for polynomials, is the central theme of this book. It has many interesting properties, obtained by algebraic, analytic and combinatorial methods. It is the subject of several longstanding unsolved questions, such as Lehmer’s Problem (1933) and Boyd’s Conjecture (1981). This book contains a wide range of results on Mahler measure. Some of the results are very recent, such as Dimitrov’s proof of the Schinzel–Zassenhaus Conjecture. Other known results are included with new, streamlined proofs. Robinson’s Conjectures (1965) for cyclotomic integers, and their associated Cassels height function, are also discussed, for the first time in a book. One way to study algebraic integers is to associate them with combinatorial objects, such as integer matrices. In some of these combinatorial settings the analogues of several notorious open problems have been solved, and the book sets out this recent work. Many Mahler measure results are proved for restricted sets of polynomials, such as for totally real polynomials, and reciprocal polynomials of integer symmetric as well as symmetrizable matrices. For reference, the book includes appendices providing necessary background from algebraic number theory, graph theory, and other prerequisites, along with tables of one- and two-variable integer polynomials with small Mahler measure. All theorems are well motivated and presented in an accessible way. Numerous exercises at various levels are given, including some for computer programming. A wide range of stimulating open problems is also included. At the end of each chapter there is a glossary of newly introduced concepts and definitions. Around the Unit Circle is written in a friendly, lucid, enjoyable style, without sacrificing mathematical rigour. It is intended for lecture courses at the graduate level, and will also be a valuable reference for researchers interested in Mahler measure. Essentially self-contained, this textbook should also be accessible to well-prepared upper-level undergraduates.
Download or read book Number Theory in Progress written by Kálmán Györy and published by Walter de Gruyter. This book was released on 2012-02-13 with total page 1212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the International Conference on Number Theory organized by the Stefan Banach International Mathematical Center in Honor of the 60th Birthday of Andrzej Schinzel, Zakopane, Poland, June 30-July 9, 1997.
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 The Theory of Algebraic Numbers Second Edition written by Harry Pollard and published by American Mathematical Soc.. This book was released on 1975-12-31 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph makes available, in English, the elementary parts of classical algebraic number theory. This second edition follows closely the plan and style of the first edition. The principal changes are the correction of misprints, the expansion or simplification of some arguments, and the omission of the final chapter on units in order to make way for the introduction of some two hundred problems.
Download or read book Fundamental Number Theory with Applications written by Richard A. Mollin and published by CRC Press. This book was released on 2008-02-21 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in its coverage. New to the Second Edition • Removal of all advanced material to be even more accessible in scope • New fundamental material, including partition theory, generating functions, and combinatorial number theory • Expanded coverage of random number generation, Diophantine analysis, and additive number theory • More applications to cryptography, primality testing, and factoring • An appendix on the recently discovered unconditional deterministic polynomial-time algorithm for primality testing Taking a truly elementary approach to number theory, this text supplies the essential material for a first course on the subject. Placed in highlighted boxes to reduce distraction from the main text, nearly 70 biographies focus on major contributors to the field. The presentation of over 1,300 entries in the index maximizes cross-referencing so students can find data with ease.
Download or read book Asymptotic Properties of Polynomials with Auxiliary Conditions of Interpolation written by Joseph Leonard Walsh and published by . This book was released on 1961 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let a closed bounded point set E be given in the z-plane. Necessary and sufficient conditions are found for validity of the following: given assigned conditions of interpolation in a finite number of points: pn(zk) = Ank; there exists a sequence of polynomials pn(z) satisfying these conditions and lim sup max pn(z), z on E 1/n = (E), where (E) is the transfinite diameter of E. (Author).
Download or read book Introduction to Number Theory written by Daniel E. Flath and published by American Mathematical Soc.. This book was released on 2018-09-27 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Growing out of a course designed to teach Gauss's Disquisitiones Arithmeticae to honors-level undergraduates, Flath's Introduction to Number Theory focuses on Gauss's theory of binary quadratic forms. It is suitable for use as a textbook in a course or self-study by advanced undergraduates or graduate students who possess a basic familiarity with abstract algebra. The text treats a variety of topics from elementary number theory including the distribution of primes, sums of squares, continued factions, the Legendre, Jacobi and Kronecker symbols, the class group and genera. But the focus is on quadratic reciprocity (several proofs are given including one that highlights the p−q symmetry) and binary quadratic forms. The reader will come away with a good understanding of what Gauss intended in the Disquisitiones and Dirichlet in his Vorlesungen. The text also includes a lovely appendix by J. P. Serre titled Δ=b2−4ac. The clarity of the author's vision is matched by the clarity of his exposition. This is a book that reveals the discovery of the quadratic core of algebraic number theory. It should be on the desk of every instructor of introductory number theory as a source of inspiration, motivation, examples, and historical insight.
Download or read book Number Theory written by Daniel Duverney and published by World Scientific. This book was released on 2010 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. 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.
