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Author: Pei-Chu Hu
Publisher: Walter de Gruyter
ISBN: 3110208261
Category : Mathematics
Languages : en
Pages : 541
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Book Description
The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references. From the contents: Field extensions • Algebraic numbers • Algebraic geometry • Height functions • The abc-conjecture • Roth's theorem • Subspace theorems • Vojta's conjectures • L-functions.
Author: Pei-Chu Hu
Publisher: Walter de Gruyter
ISBN: 3110208261
Category : Mathematics
Languages : en
Pages : 541
Get Book Here
Book Description
The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references. From the contents: Field extensions • Algebraic numbers • Algebraic geometry • Height functions • The abc-conjecture • Roth's theorem • Subspace theorems • Vojta's conjectures • L-functions.
Author: Benjamin Fine
Publisher: Springer Science & Business Media
ISBN: 0817645411
Category : Mathematics
Languages : en
Pages : 350
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Book Description
This book provides an introduction and overview of number theory based on the distribution and properties of primes. This unique approach provides both a firm background in the standard material as well as an overview of the whole discipline. All the essential topics are covered: fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. Analytic number theory and algebraic number theory both receive a solid introductory treatment. The book’s user-friendly style, historical context, and wide range of exercises make it ideal for self study and classroom use.
Author: Wladyslaw Narkiewicz
Publisher: Springer Science & Business Media
ISBN: 3662070014
Category : Mathematics
Languages : en
Pages : 712
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Book Description
This book details the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. Coverage includes: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic fields, and factorization problems. The book also features exercises and a list of open problems.
Author: Harry Pollard
Publisher: American Mathematical Soc.
ISBN: 1614440093
Category : Algebraic number theory
Languages : en
Pages : 162
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Book Description
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.
Author: Daniel A. Marcus
Publisher: Springer
ISBN: 3319902334
Category : Mathematics
Languages : en
Pages : 203
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Book Description
Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore avoids local methods and presents proofs in a way that highlights the important parts of the arguments. Readers are assumed to be able to fill in the details, which in many places are left as exercises.
Author: H. P. F. Swinnerton-Dyer
Publisher: Cambridge University Press
ISBN: 9780521004237
Category : Mathematics
Languages : en
Pages : 164
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Book Description
Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Author: Pei-Chu Hu
Publisher: Springer Science & Business Media
ISBN: 3764375698
Category : Mathematics
Languages : en
Pages : 546
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Book Description
The subject of the book is Diophantine approximation and Nevanlinna theory. This book proves not just some new results and directions but challenging open problems in Diophantine approximation and Nevanlinna theory. The authors’ newest research activities on these subjects over the past eight years are collected here. Some of the significant findings are the proof of Green-Griffiths conjecture by using meromorphic connections and Jacobian sections, generalized abc-conjecture, and more.
Author: W Narkiewicz
Publisher: World Scientific Publishing Company
ISBN: 9813104090
Category : Mathematics
Languages : en
Pages : 384
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Book Description
The aim of this book is to familiarize the reader with fundamental topics in number theory: theory of divisibility, arithmetrical functions, prime numbers, geometry of numbers, additive number theory, probabilistic number theory, theory of Diophantine approximations and algebraic number theory. The author tries to show the connection between number theory and other branches of mathematics with the resultant tools adopted in the book ranging from algebra to probability theory, but without exceeding the undergraduate students who wish to be acquainted with number theory, graduate students intending to specialize in this field and researchers requiring the present state of knowledge.
Author: Legh Wilber Reid
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 486
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Book Description
Author: Harry Pollard
Publisher:
ISBN:
Category : Algebraic fields
Languages : en
Pages : 168
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Book Description
