An Invitation To Algebraic Numbers And Algebraic Functions, Halter-Koch, Franz

Автор: Watrous, John (university Of Waterloo, Ontario)
Название: The theory of quantum information
ISBN: 1107180562 ISBN-13(EAN): 9781107180567
Издательство: Cambridge Academ
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Цена: 77090.00 T
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Описание: Intended for graduate students and researchers, this book presents a formal development of the mathematical theory of quantum information. Largely self-contained, with clear proofs and a wide range of exercises, it will help the reader grasp the fundamental facts and techniques that form the mathematical foundations of the subject.

Автор: Paulo Ribenboim
Название: Classical Theory of Algebraic Numbers
ISBN: 1441928707 ISBN-13(EAN): 9781441928702
Издательство: Springer
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Цена: 69870.00 T
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Описание: This book has a clear and thorough exposition of the classical theory of algebraic numbers, and contains a large number of exercises as well as worked out numerical examples. The introduction is a recapitulation of results about principal ideal domains, unique factorization domains and commutative fields. Part one is devoted to residue classes and quadratic residues. In part two one finds the study of algebraic integers, ideals, units, class numbers, the theory of decomposition, inertia and ramification of ideals. part three is devoted to Kummers theory of cyclotomic fields, and includes Bernoulli numbers and the proof of Fermats Last Theorem for regular prime exponents. Finally, in part four, the emphasis is on analytical methods and it includes Dirichlets Theorem on primes in arithmetic progressions, the theorem of Chebotarev and class number formulas. A careful study of this book will provide a solid background to the learning of more recent topics, as suggested at the end of the book.

Автор: Halter-Koch, Franz
Название: An Invitation to Algebraic Numbers and Algebraic Functions
ISBN: 1138583588 ISBN-13(EAN): 9781138583580
Издательство: Taylor&Francis
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Цена: 117390.00 T
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Описание: Through a set of related yet distinct texts, the author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions: Ideal- and valuation-theoretic aspects, L functions and class field theory, with a presentation of algebraic foundations which are usually undersized in standard algebra courses.

Автор: J.L. Lehman
Название: Quadratic Number Theory: An Invitation to Algebraic Methods in the Higher Arithmetic
ISBN: 1470447371 ISBN-13(EAN): 9781470447373
Издательство: Mare Nostrum (Eurospan)
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Цена: 54340.00 T
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Описание: This text is an introduction to algebraic number theory for readers with a moderate knowledge of elementary number theory and some familiarity with the terminology of abstract algebra. With its exceptionally clear prose, hundreds of exercises, and historical motivation, it would make an excellent textbook for a second undergraduate course in number theory or a terrific choice for independent reading.

Автор: Tretkoff, Paula B.
Название: Periods and special functions in transcendence
ISBN: 1786342944 ISBN-13(EAN): 9781786342942
Издательство: World Scientific Publishing
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Цена: 85530.00 T
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Описание: 'The book is mainly addressed to the non-expert reader, in that it assumes only a little background in complex analysis and algebraic geometry, but no previous knowledge in transcendental number theory is required. The technical language is introduced smoothly, and illustrative examples are provided where appropriate ... The book is carefully written, and the relevant literature is provided in the list of references. 'Mathematical Reviews ClippingsThis book gives an introduction to some central results in transcendental number theory with application to periods and special values of modular and hypergeometric functions. It also includes related results on Calabi-Yau manifolds. Most of the material is based on the author's own research and appears for the first time in book form. It is presented with minimal of technical language and no background in number theory is needed. In addition, except the last chapter, all chapters include exercises suitable for graduate students. It is a nice book for graduate students and researchers interested in transcendence.

Автор: Eric S. Egge
Название: An Introduction to Symmetric Functions and Their Combinatorics
ISBN: 1470448998 ISBN-13(EAN): 9781470448998
Издательство: Mare Nostrum (Eurospan)
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Цена: 49330.00 T
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Описание: This book is a reader-friendly introduction to the theory of symmetric functions, and it includes fundamental topics such as the monomial, elementary, homogeneous, and Schur function bases; the skew Schur functions; the Jacobi-Trudi identities; the involution $\omega$; the Hall inner product; Cauchy's formula; the RSK correspondence and how to implement it with both insertion and growth diagrams; the Pieri rules; the Murnaghan-Nakayama rule; Knuth equivalence; jeu de taquin; and the Littlewood-Richardson rule. The book also includes glimpses of recent developments and active areas of research, including Grothendieck polynomials, dual stable Grothendieck polynomials, Stanley's chromatic symmetric function, and Stanley's chromatic tree conjecture. Written in a conversational style, the book contains many motivating and illustrative examples. Whenever possible it takes a combinatorial approach, using bijections, involutions, and combinatorial ideas to prove algebraic results.The prerequisites for this book are minimal-familiarity with linear algebra, partitions, and generating functions is all one needs to get started. This makes the book accessible to a wide array of undergraduates interested in combinatorics.

Автор: Wladyslaw Narkiewicz
Название: Elementary and Analytic Theory of Algebraic Numbers
ISBN: 3642060102 ISBN-13(EAN): 9783642060106
Издательство: Springer
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Цена: 121070.00 T
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Описание: The aim of this book is to present an exposition of the theory of alge- braic numbers, excluding class-field theory and its consequences. There are many ways to develop this subject; the latest trend is to neglect the classical Dedekind theory of ideals in favour of local methods. However, for numeri- cal computations, necessary for applications of algebraic numbers to other areas of number theory, the old approach seems more suitable, although its exposition is obviously longer. On the other hand the local approach is more powerful for analytical purposes, as demonstrated in Tate's thesis. Thus the author has tried to reconcile the two approaches, presenting a self-contained exposition of the classical standpoint in the first four chapters, and then turning to local methods. In the first chapter we present the necessary tools from the theory of Dedekind domains and valuation theory, including the structure of finitely generated modules over Dedekind domains. In Chapters 2, 3 and 4 the clas- sical theory of algebraic numbers is developed. Chapter 5 contains the fun- damental notions of the theory of p-adic fields, and Chapter 6 brings their applications to the study of algebraic number fields. We include here Shafare- vich's proof of the Kronecker-Weber theorem, and also the main properties of adeles and ideles.

Автор: W?adys?aw Narkiewicz
Название: The Story of Algebraic Numbers in the First Half of the 20th Century
ISBN: 3030037533 ISBN-13(EAN): 9783030037536
Издательство: Springer
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Цена: 93160.00 T
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Описание: The book is aimed at people working in number theory or at least interested in this part of mathematics. It presents the development of the theory of algebraic numbers up to the year 1950 and contains a rather complete bibliography of that period. The reader will get information about results obtained before 1950. It is hoped that this may be helpful in preventing rediscoveries of old results, and might also inspire the reader to look at the work done earlier, which may hide some ideas which could be applied in contemporary research.

Автор: Hitoshi Konno, Hidetaka Sakai, Junichi Shiraishi, Takao Suzuki, Yasuhiko Yamada
Название: Representation Theory, Special Functions and Painvleve Equations - RIMS 2015
ISBN: 4864970505 ISBN-13(EAN): 9784864970501
Издательство: Mare Nostrum (Eurospan)
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Цена: 97020.00 T
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Описание: Contains 15 papers covering a variety of topics in the research fields where Masatoshi Noumi has made significant contributions over the years - representation theory, special functions, Painleve equations, among others.

Автор: Dihua Jiang, Freydoon Shahidi, David Soudry
Название: Advances in the Theory of Automorphic Forms and Their $L$-functions
ISBN: 147041709X ISBN-13(EAN): 9781470417093
Издательство: Mare Nostrum (Eurospan)
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Цена: 108110.00 T
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Описание: This volume contains the proceedings of the workshop on ``Advances in the Theory of Automorphic Forms and Their $L$-functions'' held in honor of James Cogdell's 60th birthday, held from October 16-25, 2013, at the Erwin Schrodinger Institute (ESI) at the University of Vienna.The workshop and the papers contributed to this volume circle around such topics as the theory of automorphic forms and their $L$-functions, geometry and number theory, covering some of the recent approaches and advances to these subjects. Specifically, the papers cover aspects of representation theory of $p$-adic groups, classification of automorphic representations through their Fourier coefficients and their liftings, $L$-functions for classical groups, special values of $L$-functions, Howe duality, subconvexity for $L$-functions, Kloosterman integrals, arithmetic geometry and cohomology of arithmetic groups, and other important problems on $L$-functions, nodal sets and geometry.

Автор: Trifkovic Mak
Название: Algebraic Theory of Quadratic Numbers
ISBN: 1461477166 ISBN-13(EAN): 9781461477167
Издательство: Springer
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Цена: 55890.00 T
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Описание: This book shows the techniques of elementary arithmetic, ring theory and linear algebra working together to prove important theorems, such as the unique factorization of ideals and the finiteness of the ideal class group. Includes numerous exercises.