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Author : 中村博昭
Publisher :
ISBN 13 :
Total Pages : 336 pages
Book Rating : 4.:/5 (8 download)
Download or read book Algebraic Number Theory and Related Topics 2008 written by 中村博昭 and published by . This book was released on 2010 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pierre Samuel
Publisher : Dover Books on Mathematics
ISBN 13 : 9780486466668
Total Pages : 0 pages
Book Rating : 4.4/5 (666 download)
Download or read book Algebraic Theory of Numbers written by Pierre Samuel and published by Dover Books on Mathematics. This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic number theory introduces students to new algebraic notions as well as related concepts: groups, rings, fields, ideals, quotient rings, and quotient fields. This text covers the basics, from divisibility theory in principal ideal domains to the unit theorem, finiteness of the class number, and Hilbert ramification theory. 1970 edition.
Author : 中村博昭
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (73 download)
Download or read book Algebraic number theory and related topics 2008 : December 8 - 12, 2008 written by 中村博昭 and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Serge Lang
Publisher : Springer Science & Business Media
ISBN 13 : 146120853X
Total Pages : 356 pages
Book Rating : 4.4/5 (612 download)
Download or read book Algebraic Number Theory written by Serge Lang and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary for the study of further topics in algebraic number theory, such as cyclotomic fields, or modular forms. "Lang's books are always of great value for the graduate student and the research mathematician. This updated edition of Algebraic number theory is no exception."—-MATHEMATICAL REVIEWS
Author : Henry Berthold Mann
Publisher :
ISBN 13 :
Total Pages : 190 pages
Book Rating : 4.:/5 (5 download)
Download or read book Introduction to Algebraic Number Theory written by Henry Berthold Mann and published by . This book was released on 1955 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : M. Ram Murty
Publisher : Springer Science & Business Media
ISBN 13 : 0387221824
Total Pages : 354 pages
Book Rating : 4.3/5 (872 download)
Download or read book Problems in Algebraic Number Theory written by M. Ram Murty and published by Springer Science & Business Media. This book was released on 2005 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challenging All problems are elegantly solved
Author : Edwin Weiss
Publisher : Courier Corporation
ISBN 13 : 048615436X
Total Pages : 308 pages
Book Rating : 4.4/5 (861 download)
Download or read book Algebraic Number Theory written by Edwin Weiss and published by Courier Corporation. This book was released on 2012-01-27 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal either for classroom use or as exercises for mathematically minded individuals, this text introduces elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields.
Author : Helmut Koch
Publisher : American Mathematical Soc.
ISBN 13 : 9780821820544
Total Pages : 390 pages
Book Rating : 4.8/5 (25 download)
Download or read book Number Theory written by Helmut Koch and published by American Mathematical Soc.. This book was released on 2000 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic number theory is one of the most refined creations in mathematics. It has been developed by some of the leading mathematicians of this and previous centuries. The primary goal of this book is to present the essential elements of algebraic number theory, including the theory of normal extensions up through a glimpse of class field theory. Following the example set for us by Kronecker, Weber, Hilbert and Artin, algebraic functions are handled here on an equal footing with algebraic numbers. This is done on the one hand to demonstrate the analogy between number fields and function fields, which is especially clear in the case where the ground field is a finite field. On the other hand, in this way one obtains an introduction to the theory of 'higher congruences' as an important element of 'arithmetic geometry'. Early chapters discuss topics in elementary number theory, such as Minkowski's geometry of numbers, public-key cryptography and a short proof of the Prime Number Theorem, following Newman and Zagier. Next, some of the tools of algebraic number theory are introduced, such as ideals, discriminants and valuations. These results are then applied to obtain results about function fields, including a proof of the Riemann-Roch Theorem and, as an application of cyclotomic fields, a proof of the first case of Fermat's Last Theorem. There are a detailed exposition of the theory of Hecke $L$-series, following Tate, and explicit applications to number theory, such as the Generalized Riemann Hypothesis. Chapter 9 brings together the earlier material through the study of quadratic number fields. Finally, Chapter 10 gives an introduction to class field theory. The book attempts as much as possible to give simple proofs. It can be used by a beginner in algebraic number theory who wishes to see some of the true power and depth of the subject. The book is suitable for two one-semester courses, with the first four chapters serving to develop the basic material. Chapters 6 through 9 could be used on their own as a second semester course.
Download or read book Algebraic number theory and related topics written by and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jürgen Neukirch
Publisher : Springer
ISBN 13 : 9783642084737
Total Pages : 0 pages
Book Rating : 4.0/5 (847 download)
Download or read book Algebraic Number Theory written by Jürgen Neukirch and published by Springer. This book was released on 2010-12-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to algebraic number theory discusses the classical concepts from the viewpoint of Arakelov theory. The treatment of class theory is particularly rich in illustrating complements, offering hints for further study, and providing concrete examples. It is the most up-to-date, systematic, and theoretically comprehensive textbook on algebraic number field theory available.
Author : Ian Stewart
Publisher : CRC Press
ISBN 13 : 1498738400
Total Pages : 338 pages
Book Rating : 4.4/5 (987 download)
Download or read book Algebraic Number Theory and Fermat's Last Theorem written by Ian Stewart and published by CRC Press. This book was released on 2015-10-14 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Updated to reflect current research, Algebraic Number Theory and Fermat’s Last Theorem, Fourth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematics—the quest for a proof of Fermat’s Last Theorem. The authors use this celebrated theorem to motivate a general study of the theory of algebraic numbers from a relatively concrete point of view. Students will see how Wiles’s proof of Fermat’s Last Theorem opened many new areas for future work. New to the Fourth Edition Provides up-to-date information on unique prime factorization for real quadratic number fields, especially Harper’s proof that Z(√14) is Euclidean Presents an important new result: Mihăilescu’s proof of the Catalan conjecture of 1844 Revises and expands one chapter into two, covering classical ideas about modular functions and highlighting the new ideas of Frey, Wiles, and others that led to the long-sought proof of Fermat’s Last Theorem Improves and updates the index, figures, bibliography, further reading list, and historical remarks Written by preeminent mathematicians Ian Stewart and David Tall, this text continues to teach students how to extend properties of natural numbers to more general number structures, including algebraic number fields and their rings of algebraic integers. It also explains how basic notions from the theory of algebraic numbers can be used to solve problems in number theory.
Author : Takashi Aoki
Publisher : World Scientific
ISBN 13 : 9814289922
Total Pages : 267 pages
Book Rating : 4.8/5 (142 download)
Download or read book Number Theory written by Takashi Aoki and published by World Scientific. This book was released on 2010 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume aims at collecting survey papers which give broad and enlightening perspectives of various aspects of number theory. Kitaoka''s paper is a continuation of his earlier paper published in the last proceedings and pushes the research forward. Browning''s paper introduces a new direction of research on analytic number theory OCo quantitative theory of some surfaces and Bruedern et al ''s paper details state-of-the-art affairs of additive number theory. There are two papers on modular forms OCo Kohnen''s paper describes generalized modular forms (GMF) which has some applications in conformal field theory, while Liu''s paper is very useful for readers who want to have a quick introduction to Maass forms and some analytic-number-theoretic problems related to them. Matsumoto et al ''s paper gives a very thorough survey on functional relations of root system zeta-functions, HoshiOCoMiyake''s paper is a continuation of Miyake''s long and fruitful research on generic polynomials and gives rise to related Diophantine problems, and Jia''s paper surveys some dynamical aspects of a special arithmetic function connected with the distribution of prime numbers. There are two papers of collections of problems by Shparlinski on exponential and character sums and Schinzel on polynomials which will serve as an aid for finding suitable research problems. Yamamura''s paper is a complete bibliography on determinant expressions for a certain class number and will be useful to researchers. Thus the book gives a good-balance of classical and modern aspects in number theory and will be useful to researchers including enthusiastic graduate students. Sample Chapter(s). Chapter 1: Resent Progress on the Quantitative Arithmetic of Del Pezzo Surfaces (329 KB). Contents: Recent Progress on the Quantitative Arithmetic of Del Pezzo Surfaces (T D Browning); Additive Representation in Thin Sequences, VIII: Diophantine Inequalities in Review (J Brdern et al.); Recent Progress on Dynamics of a Special Arithmetic Function (C-H Jia); Some Diophantine Problems Arising from the Isomorphism Problem of Generic Polynomials (A Hoshi & K Miyake); A Statistical Relation of Roots of a Polynomial in Different Local Fields II (Y Kitaoka); Generalized Modular Functions and Their Fourier Coefficients (W Kohnen); Functional Relations for Zeta-Functions of Root Systems (Y Komori et al.); A Quick Introduction to Maass Forms (J-Y Liu); The Number of Non-Zero Coefficients of a Polynomial-Solved and Unsolved Problems (A Schinzel); Open Problems on Exponential and Character Sums (I E Shparlinski); Errata to OC A General Modular Relation in Analytic Number TheoryOCO (H Tsukada); Bibliography on Determinantal Expressions of Relative Class Numbers of Imaginary Abelian Number Fields (K Yamamura). Readership: Graduate students and researchers in mathematics.
Author : Sudesh Kaur Khanduja
Publisher : Springer Nature
ISBN 13 : 9811691509
Total Pages : 261 pages
Book Rating : 4.8/5 (116 download)
Download or read book A Textbook of Algebraic Number Theory written by Sudesh Kaur Khanduja and published by Springer Nature. This book was released on 2022-04-26 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained and comprehensive textbook of algebraic number theory is useful for advanced undergraduate and graduate students of mathematics. The book discusses proofs of almost all basic significant theorems of algebraic number theory including Dedekind’s theorem on splitting of primes, Dirichlet’s unit theorem, Minkowski’s convex body theorem, Dedekind’s discriminant theorem, Hermite’s theorem on discriminant, Dirichlet’s class number formula, and Dirichlet’s theorem on primes in arithmetic progressions. A few research problems arising out of these results are mentioned together with the progress made in the direction of each problem. Following the classical approach of Dedekind’s theory of ideals, the book aims at arousing the reader’s interest in the current research being held in the subject area. It not only proves basic results but pairs them with recent developments, making the book relevant and thought-provoking. Historical notes are given at various places. Featured with numerous related exercises and examples, this book is of significant value to students and researchers associated with the field. The book also is suitable for independent study. The only prerequisite is basic knowledge of abstract algebra and elementary number theory.
Author : Gradimir V. Milovanović
Publisher : Springer
ISBN 13 : 149390258X
Total Pages : 873 pages
Book Rating : 4.4/5 (939 download)
Download or read book Analytic Number Theory, Approximation Theory, and Special Functions written by Gradimir V. Milovanović and published by Springer. This book was released on 2014-07-08 with total page 873 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics and other computational and applied sciences.
Author : Ian Stewart
Publisher : Springer
ISBN 13 :
Total Pages : 296 pages
Book Rating : 4.3/5 (91 download)
Download or read book Algebraic Number Theory written by Ian Stewart and published by Springer. This book was released on 1987-05-07 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Noriyuki Suwa
Publisher :
ISBN 13 :
Total Pages : 245 pages
Book Rating : 4.:/5 (935 download)
Download or read book Algebraic Number Theory and Related Topics 2011 written by Noriyuki Suwa and published by . This book was released on 2013 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Richard A. Mollin
Publisher : Chapman and Hall/CRC
ISBN 13 : 9781439845981
Total Pages : 0 pages
Book Rating : 4.8/5 (459 download)
Download or read book Algebraic Number Theory, Second Edition written by Richard A. Mollin and published by Chapman and Hall/CRC. This book was released on 2011-01-05 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bringing the material up to date to reflect modern applications, Algebraic Number Theory, Second Edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation. This edition focuses on integral domains, ideals, and unique factorization in the first chapter; field extensions in the second chapter; and class groups in the third chapter. Applications are now collected in chapter four and at the end of chapter five, where primality testing is highlighted as an application of the Kronecker–Weber theorem. In chapter five, the sections on ideal decomposition in number fields have been more evenly distributed. The final chapter continues to cover reciprocity laws. New to the Second Edition Reorganization of all chapters More complete and involved treatment of Galois theory A study of binary quadratic forms and a comparison of the ideal and form class groups More comprehensive section on Pollard’s cubic factoring algorithm More detailed explanations of proofs, with less reliance on exercises, to provide a sound understanding of challenging material The book includes mini-biographies of notable mathematicians, convenient cross-referencing, a comprehensive index, and numerous exercises. The appendices present an overview of all the concepts used in the main text, an overview of sequences and series, the Greek alphabet with English transliteration, and a table of Latin phrases and their English equivalents. Suitable for a one-semester course, this accessible, self-contained text offers broad, in-depth coverage of numerous applications. Readers are lead at a measured pace through the topics to enable a clear understanding of the pinnacles of algebraic number theory.
