Auxiliary Polynomials In Number Theory
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Auxiliary Polynomials In Number Theory
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Author : David Masser
language : en
Publisher: Cambridge University Press
Release Date : 2016-07-21
Auxiliary Polynomials In Number Theory written by David Masser and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-21 with Mathematics categories.
A unified account of a powerful classical method, illustrated by applications in number theory. Aimed at graduates and professionals.
Auxiliary Polynomials In Number Theory
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Author : David Masser
language : en
Publisher: Cambridge University Press
Release Date : 2016-07-21
Auxiliary Polynomials In Number Theory written by David Masser and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-21 with Mathematics categories.
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.
Number Theory And Polynomials
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Author : James Fraser McKee
language : en
Publisher: Cambridge University Press
Release Date : 2008-05-08
Number Theory And Polynomials written by James Fraser McKee and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-08 with Mathematics categories.
Contributions by leading experts in the field provide a snapshot of current progress in polynomials and number theory.
Number Theory With Computations
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Author : Peter Shiu
language : en
Publisher: Springer Nature
Release Date : 2024-09-02
Number Theory With Computations written by Peter Shiu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-02 with Mathematics categories.
This introductory text is designed for undergraduate courses in number theory, covering both elementary number theory and analytic number theory. The book emphasises computational aspects, including algorithms and their implementation in Python. The book is divided into two parts. The first part, on elementary number theory, deals with concepts such as induction, divisibility, congruences, primitive roots, cryptography, and continued fractions. The second part is devoted to analytic number theory and includes chapters on Dirichlet’s theorem on primes in arithmetic progressions, the prime number theorem, smooth numbers, and the famous circle method of Hardy and Littlewood. The book contains many topics not often found in introductory textbooks, such as Aubry’s theorem, the Tonelli–Shanks algorithm, factorisation methods, continued fraction representations of e, and the irrationality of ζ(3). Each chapter concludes with a summary and notes, as well as numerous exercises. Assuming only basic calculus for the first part of the book, the second part assumes some knowledge of complex analysis. Familiarity with basic coding syntax will be helpful for the computational exercises.
Polynomial Methods In Combinatorics
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Author : Larry Guth
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-06-10
Polynomial Methods In Combinatorics written by Larry Guth and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-10 with Mathematics categories.
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.
Analytic Number Theory And Diophantine Problems
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Author : A.C. Adolphson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Analytic Number Theory And Diophantine Problems written by A.C. Adolphson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A conference on Analytic Number Theory and Diophantine Problems was held from June 24 to July 3, 1984 at the Oklahoma State University in Stillwater. The conference was funded by the National Science Foundation, the College of Arts and Sciences and the Department of Mathematics at Oklahoma State University. The papers in this volume represent only a portion of the many talks given at the conference. The principal speakers were Professors E. Bombieri, P. X. Gallagher, D. Goldfeld, S. Graham, R. Greenberg, H. Halberstam, C. Hooley, H. Iwaniec, D. J. Lewis, D. W. Masser, H. L. Montgomery, A. Selberg, and R. C. Vaughan. Of these, Professors Bombieri, Goldfeld, Masser, and Vaughan gave three lectures each, while Professor Hooley gave two. Special sessions were also held and most participants gave talks of at least twenty minutes each. Prof. P. Sarnak was unable to attend but a paper based on his intended talk is included in this volume. We take this opportunity to thank all participants for their (enthusiastic) support for the conference. Judging from the response, it was deemed a success. As for this volume, I take responsibility for any typographical errors that may occur in the final print. I also apologize for the delay (which was due to the many problems incurred while retyping all the papers). A. special thanks to Dollee Walker for retyping the papers and to Prof. W. H. Jaco for his support, encouragement and hard work in bringing the idea of the conference to fruition.
Transcendental Number Theory
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Author : Alan Baker
language : en
Publisher: Cambridge University Press
Release Date : 1990-09-28
Transcendental Number Theory written by Alan Baker and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-09-28 with Mathematics categories.
First published in 1975, this classic book gives a systematic account of transcendental number theory, that is those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory enriching many branches of pure mathematics. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalisation of the Thue-Siegel-Roth theorem, of Shidlovsky's work on Siegel's |E|-functions and of Sprindzuk's solution to the Mahler conjecture. The volume was revised in 1979: however Professor Baker has taken this further opportunity to update the book including new advances in the theory and many new references.
Unit Equations In Diophantine Number Theory
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Author : Jan-Hendrik Evertse
language : en
Publisher: Cambridge University Press
Release Date : 2015-12-30
Unit Equations In Diophantine Number Theory written by Jan-Hendrik Evertse and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-30 with Mathematics categories.
A comprehensive, graduate-level treatment of unit equations and their various applications.
Lectures On Contact 3 Manifolds Holomorphic Curves And Intersection Theory
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Author : Chris Wendl
language : en
Publisher: Cambridge University Press
Release Date : 2020-03-26
Lectures On Contact 3 Manifolds Holomorphic Curves And Intersection Theory written by Chris Wendl and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-26 with Mathematics categories.
An accessible introduction to the intersection theory of punctured holomorphic curves and its applications in topology.
Around The Unit Circle
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Author : James McKee
language : en
Publisher: Springer Nature
Release Date : 2021-12-08
Around The Unit Circle written by James McKee and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-08 with Mathematics categories.
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.