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Topics in the Theory of Algebraic Function Fields

2007-10-10 Mathematics
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Release : 2007-10-10
Genre : Mathematics
Kind : eBook
Book Rating : 152/5 ( reviews)

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Book Synopsis Topics in the Theory of Algebraic Function Fields by : Gabriel Daniel Villa Salvador

Download or read book Topics in the Theory of Algebraic Function Fields written by Gabriel Daniel Villa Salvador. This book was released on 2007-10-10. Available in PDF, EPUB and Kindle. Book excerpt: 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 Function Fields and Codes

2009-02-11 Mathematics
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Release : 2009-02-11
Genre : Mathematics
Kind : eBook
Book Rating : 785/5 ( reviews)

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Book Synopsis Algebraic Function Fields and Codes by : Henning Stichtenoth

Download or read book Algebraic Function Fields and Codes written by Henning Stichtenoth. This book was released on 2009-02-11. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Number Theory in Function Fields

2013-04-18 Mathematics
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Release : 2013-04-18
Genre : Mathematics
Kind : eBook
Book Rating : 469/5 ( reviews)

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Book Synopsis Number Theory in Function Fields by : Michael Rosen

Download or read book Number Theory in Function Fields written by Michael Rosen. This book was released on 2013-04-18. Available in PDF, EPUB and Kindle. Book excerpt: Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field. The first part of this book illustrates this relationship by presenting analogues of various theorems. The later chapters probe the analogy between global function fields and algebraic number fields. Topics include the ABC-conjecture, Brumer-Stark conjecture, and Drinfeld modules.

Introduction to the Theory of Algebraic Functions of One Variable

1951-12-31 Mathematics
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Release : 1951-12-31
Genre : Mathematics
Kind : eBook
Book Rating : 067/5 ( reviews)

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Book Synopsis Introduction to the Theory of Algebraic Functions of One Variable by : Claude Chevalley

Download or read book Introduction to the Theory of Algebraic Functions of One Variable written by Claude Chevalley. This book was released on 1951-12-31. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Functions and Projective Curves

2006-04-06 Mathematics
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Release : 2006-04-06
Genre : Mathematics
Kind : eBook
Book Rating : 459/5 ( reviews)

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Book Synopsis Algebraic Functions and Projective Curves by : David Goldschmidt

Download or read book Algebraic Functions and Projective Curves written by David Goldschmidt. This book was released on 2006-04-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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