The Theory of Algebraic Number Fields, David Hilbert; F. Lemmermeyer; I.T. Adamson; N. Sc
Автор: H. P. F. Swinnerton-Dyer Название: A Brief Guide to Algebraic Number Theory ISBN: 0521004233 ISBN-13(EAN): 9780521004237 Издательство: Cambridge Academ Рейтинг: Цена: 7762.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A 2001 account of Algebraic Number Theory, a field which has grown to touch many other areas of pure mathematics. Encompasses everything that graduate students and pure mathematicians interested in the subject are likely to need. Many exercises and an annotated reading list are included.
Автор: Neukirch Название: Algebraic Number Theory ISBN: 3540653996 ISBN-13(EAN): 9783540653998 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Aims to provide an introduction to algebraic number theory, which is largely based on the conception of (one-dimensional) arithmetic algebraic geometry. This book discusses the classical concepts from the viewpoint of Arakelov theory. It concludes with a chapter on zeta-functions and L-series.
Описание: The circle method has its genesis in a paper of Hardy and Ramanujan (see Hardy 1])in 1918concernedwiththepartitionfunction andtheproblemofrep- resenting numbers as sums ofsquares. Later, in a series of papers beginning in 1920entitled "some problems of'partitio numerorum''', Hardy and Littlewood (see Hardy 1]) created and developed systematically a new analytic method, the circle method in additive number theory. The most famous problems in ad- ditive number theory, namely Waring's problem and Goldbach's problem, are treated in their papers. The circle method is also called the Hardy-Littlewood method. Waring's problem may be described as follows: For every integer k 2 2, there is a number s= s( k) such that every positive integer N is representable as (1) where Xi arenon-negative integers. This assertion wasfirst proved by Hilbert 1] in 1909. Using their powerful circle method, Hardy and Littlewood obtained a deeper result on Waring's problem. They established an asymptotic formula for rs(N), the number of representations of N in the form (1), namely k 1 provided that 8 2 (k - 2)2 - +5. Here
Автор: Baruch Z. Moroz Название: Analytic Arithmetic in Algebraic Number Fields ISBN: 3540167846 ISBN-13(EAN): 9783540167846 Издательство: Springer Рейтинг: Цена: 3487.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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.
Автор: Serge Lang Название: Algebraic Number Theory ISBN: 0387942254 ISBN-13(EAN): 9780387942254 Издательство: Springer Рейтинг: Цена: 8384.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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.
Автор: Henri Cohen Название: A Course in Computational Algebraic Number Theory ISBN: 3642081428 ISBN-13(EAN): 9783642081422 Издательство: Springer Рейтинг: Цена: 9077.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: With the advent of powerful computing tools and numerous advances in math- ematics, computer science and cryptography, algorithmic number theory has become an important subject in its own right. Both external and internal pressures gave a powerful impetus to the development of more powerful al- gorithms. These in turn led to a large number of spectacular breakthroughs. To mention but a few, the LLL algorithm which has a wide range of appli- cations, including real world applications to integer programming, primality testing and factoring algorithms, sub-exponential class group and regulator algorithms, etc ... Several books exist which treat parts of this subject. (It is essentially impossible for an author to keep up with the rapid pace of progress in all areas of this subject.) Each book emphasizes a different area, corresponding to the author's tastes and interests. The most famous, but unfortunately the oldest, is Knuth's Art of Computer Programming, especially Chapter 4. The present book has two goals. First, to give a reasonably comprehensive introductory course in computational number theory. In particular, although we study some subjects in great detail, others are only mentioned, but with suitable pointers to the literature. Hence, we hope that this book can serve as a first course on the subject. A natural sequel would be to study more specialized subjects in the existing literature.
Автор: M.E. Pohst Название: Computational Algebraic Number Theory ISBN: 3764329130 ISBN-13(EAN): 9783764329136 Издательство: Springer Рейтинг: Цена: 4186.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Computational algebraic number theory has been attracting broad interest in the last few years due to its potential applications in coding theory and cryptography. This book emphasizes practical algorithms for the computation of integral bases, the unit group and the class group of arbitrary algebraic number fields.
Автор: Hussein Mourtada; Celal Cem Sar?o?lu; Christophe S Название: Algebraic Geometry and Number Theory ISBN: 3319477781 ISBN-13(EAN): 9783319477787 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This lecture notes volume presents significant contributions from the "Algebraic Geometry and Number Theory" Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014.It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology.
Автор: Murty M. Ram Название: Problems in Algebraic Number Theory ISBN: 1441919678 ISBN-13(EAN): 9781441919670 Издательство: Springer Рейтинг: Цена: 9781.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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
Автор: Valentin Blomer; Preda Mih?ilescu Название: Contributions in Analytic and Algebraic Number Theory ISBN: 1489991581 ISBN-13(EAN): 9781489991584 Издательство: Springer Рейтинг: Цена: 25853.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The text that comprises this volume is a collection of surveys and original works from experts in the fields of algebraic number theory, analytic number theory, harmonic analysis, and hyperbolic geometry.
Автор: J?rgen Neukirch; Norbert Schappacher Название: Algebraic Number Theory ISBN: 3642084737 ISBN-13(EAN): 9783642084737 Издательство: Springer Рейтинг: Цена: 15366.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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.
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