Algebraic Functions
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Algebraic Numbers And Algebraic Functions
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Author : Emil Artin
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Algebraic Numbers And Algebraic Functions written by Emil Artin 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 2005 with Mathematics categories.
Originated from the notes of a course given at Princeton University in 1950-1951, this text offers an introduction to algebraic numbers and algebraic functions. It starts with the general theory of valuation fields, proceeds to the local class field theory, and then to the theory of function fields in one variable.
Algebraic Functions
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Author : Gilbert Ames Bliss
language : en
Publisher: American Mathematical Soc.
Release Date : 1933-12-31
Algebraic Functions written by Gilbert Ames Bliss 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 1933-12-31 with Mathematics categories.
This book, immediately striking for its conciseness, is one of the most remarkable works ever produced on the subject of algebraic functions and their integrals. The distinguishing feature of the book is its third chapter, on rational functions, which gives an extremely brief and clear account of the theory of divisors.... A very readable account is given of the topology of Riemann surfaces and of the general properties of abelian integrals. Abel's theorem is presented, with some simple applications. The inversion problem is studied for the cases of genus zero and genus unity. The chapter on the reduction of singularities is very noteworthy.... A final chapter illustrates the general theory with some examples. In particular, constructive methods are given for treating algebraic relations which are of the third degree in one of the variables.... The arithmetic theory of algebraic functions is a good thing. In making its study easy, Bliss has performed a service which will win him the gratitude of an ever increasing number of readers. --Bulletin of the American Mathematical Society
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.
On The Integration Of Algebraic Functions
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Author : James Harold Davenport
language : en
Publisher:
Release Date : 1981
On The Integration Of Algebraic Functions written by James Harold Davenport and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
Introduction To The Theory Of Algebraic Functions Of One Variable
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Author : Claude Chevalley
language : en
Publisher: American Mathematical Soc.
Release Date : 1951-12-31
Introduction To The Theory Of Algebraic Functions Of One Variable written by Claude Chevalley 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 1951-12-31 with Mathematics categories.
Presents an approach to algebraic geometry of curves that is treated as the theory of algebraic functions on the curve. This book discusses such topics as the theory of divisors on a curve, the Riemann-Roch theorem, $p$-adic completion, and extensions of the fields of functions (covering theory) and of the fields of constants.
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.
Lectures On The Theory Of Algebraic Functions Of One Variable
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Author : Max Deuring
language : en
Publisher: Lecture Notes in Mathematics
Release Date : 1973-02-19
Lectures On The Theory Of Algebraic Functions Of One Variable written by Max Deuring and has been published by Lecture Notes in Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-02-19 with Mathematics categories.
Algebraic Functions And Projective Curves
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Author : David Goldschmidt
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-06
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 2006-04-06 with Mathematics categories.
This book gives an introduction to algebraic functions and projective curves. It covers a wide range of material by dispensing with the machinery of algebraic geometry and proceeding directly via valuation theory to the main results on function fields. It also develops the theory of singular curves by studying maps to projective space, including topics such as Weierstrass points in characteristic p, and the Gorenstein relations for singularities of plane curves.
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.
Semi Algebraic Function Rings And Reflectors Of Partially Ordered Rings
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Author : Niels Schwartz
language : en
Publisher: Springer
Release Date : 2006-11-13
Semi Algebraic Function Rings And Reflectors Of Partially Ordered Rings written by Niels Schwartz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-13 with Mathematics categories.
The book lays algebraic foundations for real geometry through a systematic investigation of partially ordered rings of semi-algebraic functions. Real spectra serve as primary geometric objects, the maps between them are determined by rings of functions associated with the spectra. The many different possible choices for these rings of functions are studied via reflections of partially ordered rings. Readers should feel comfortable using basic algebraic and categorical concepts. As motivational background some familiarity with real geometry will be helpful. The book aims at researchers and graduate students with an interest in real algebra and geometry, ordered algebraic structures, topology and rings of continuous functions.