Algebraic Function
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Algebraic Function Fields And Codes
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Author : Henning Stichtenoth
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-11
Algebraic Function Fields And Codes written by Henning Stichtenoth 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 2009-02-11 with Mathematics categories.
This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.
Topics In The Theory Of Algebraic Function Fields
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Author : Gabriel Daniel Villa Salvador
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-10
Topics In The Theory Of Algebraic Function Fields written by Gabriel Daniel Villa Salvador 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 2007-10-10 with Mathematics categories.
The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of numbers. The examination explains both the similarities and fundamental differences between function fields and number fields, including many exercises and examples to enhance understanding and motivate further study. The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra.
Algebraic Functions
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Author : Kenkichi Iwasawa
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Algebraic Functions written by Kenkichi Iwasawa 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 1993 with Mathematics categories.
This is a translation of Iwasawa's 1973 book, Theory of Algebraic Functions originally published in Japanese. Because the book treats mainly the classical part of the theory of algebraic functions, emphasizing analytic methods, it provides an excellent introduction to the subject from the classical viewpoint. Directed at graduate students, the book requires some basic knowledge of algebra, topology, and functions of a complex variable.
Algebraic Functions And Projective Curves
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Author : David Goldschmidt
language : en
Publisher: Springer Science & Business Media
Release Date : 2003
Algebraic Functions And Projective Curves written by David Goldschmidt 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 2003 with Mathematics categories.
This book grew out of a set of notes for a series of lectures I orginally gave at the Center for Communications Research and then at Princeton University. The motivation was to try to understand the basic facts about algebraic curves without the modern prerequisite machinery of algebraic geometry. Of course, one might well ask if this is a good thing to do. There is no clear answer to this question. In short, we are trading off easier access to the facts against a loss of generality and an impaired understanding of some fundamental ideas. Whether or not this is a useful tradeoff is something you will have to decide for yourself. One of my objectives was to make the exposition as self-contained as possible. Given the choice between a reference and a proof, I usually chose the latter. - though I worked out many of these arguments myself, I think I can con?dently predict that few, if any, of them are novel. I also made an effort to cover some topics that seem to have been somewhat neglected in the expository literature.
Algebraic Functions
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Author : Gilbert Ames Bliss
language : en
Publisher: Courier Corporation
Release Date : 2004-01-01
Algebraic Functions written by Gilbert Ames Bliss and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Mathematics categories.
This text surveys the approaches and basic results of all three classes of algebraic functions. Starting with a treatment of single-valued analytic functions, it introduces algebraic and rational functions and proceeds to the Riemann surface of an algebraic function, integrals of rational functions, and Abel's theorem. 1933 edition
Algebraic Numbers And Algebraic Functions
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Author : P.M. Cohn
language : en
Publisher: CRC Press
Release Date : 2018-01-18
Algebraic Numbers And Algebraic Functions written by P.M. Cohn and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-18 with Mathematics categories.
This book is an introduction to the theory of algebraic numbers and algebraic functions of one variable. The basic development is the same for both using E Artin's legant approach, via valuations. Number Theory is pursued as far as the unit theorem and the finiteness of the class number. In function theory the aim is the Abel-Jacobi theorem describing the devisor class group, with occasional geometrical asides to help understanding. Assuming only an undergraduate course in algebra, plus a little acquaintance with topology and complex function theory, the book serves as an introduction to more technical works in algebraic number theory, function theory or algebraic geometry by an exposition of the central themes in the subject.
Topics In The Theory Of Algebraic Function Fields
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Author : Gabriel Daniel Villa Salvador
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-11
Topics In The Theory Of Algebraic Function Fields written by Gabriel Daniel Villa Salvador 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 2006-07-11 with Mathematics categories.
The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of numbers. The examination explains both the similarities and fundamental differences between function fields and number fields, including many exercises and examples to enhance understanding and motivate further study. The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra.
Theory Of Algebraic Functions Of One Variable
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Author : Richard Dedekind
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-07-23
Theory Of Algebraic Functions Of One Variable written by Richard Dedekind 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 2012-07-23 with Mathematics categories.
This book is the first English translation of the classic long paper Theorie der algebraischen Functionen einer Veranderlichen (Theory of algebraic functions of one variable), published by Dedekind and Weber in 1882. The translation has been enriched by a Translator's Introduction that includes historical background, and also by extensive commentary embedded in the translation itself. The translation, introduction, and commentary provide the first easy access to this important paper for a wide mathematical audience: students, historians of mathematics, and professional mathematicians. Why is the Dedekind-Weber paper important? In the 1850s, Riemann initiated a revolution in algebraic geometry by interpreting algebraic curves as surfaces covering the sphere. He obtained deep and striking results in pure algebra by intuitive arguments about surfaces and their topology. However, Riemann's arguments were not rigorous, and they remained in limbo until 1882, when Dedekind and Weber put them on a sound foundation. The key to this breakthrough was to develop the theory of algebraic functions in analogy with Dedekind's theory of algebraic numbers, where the concept of ideal plays a central role. By introducing such concepts into the theory of algebraic curves, Dedekind and Weber paved the way for modern algebraic geometry.
Introduction To Algebraic And Abelian Functions
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 1982-12
Introduction To Algebraic And Abelian Functions written by Serge Lang 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 1982-12 with Mathematics categories.
Introduction to Algebraic and Abelian Functions is a self-contained presentation of a fundamental subject in algebraic geometry and number theory. For this revised edition, the material on theta functions has been expanded, and the example of the Fermat curves is carried throughout the text. This volume is geared toward a second-year graduate course, but it leads naturally to the study of more advanced books listed in the bibliography.
Algebraic Numbers And Algebraic Functions
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Author : Emil Artin
language : en
Publisher: CRC Press
Release Date : 1967
Algebraic Numbers And Algebraic Functions written by Emil Artin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Mathematics categories.