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Basic Structures of Function Field Arithmetic

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 809/5 ( reviews)

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Book Synopsis Basic Structures of Function Field Arithmetic by : David Goss

Download or read book Basic Structures of Function Field Arithmetic written by David Goss. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews:"The book...is a thorough and very readable introduction to the arithmetic of function fields of one variable over a finite field, by an author who has made fundamental contributions to the field. It serves as a definitive reference volume, as well as offering graduate students with a solid understanding of algebraic number theory the opportunity to quickly reach the frontiers of knowledge in an important area of mathematics...The arithmetic of function fields is a universe filled with beautiful surprises, in which familiar objects from classical number theory reappear in new guises, and in which entirely new objects play important roles. Goss'clear exposition and lively style make this book an excellent introduction to this fascinating field." MR 97i:11062

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.

Function Field Arithmetic

2004 Mathematics
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Release : 2004
Genre : Mathematics
Kind : eBook
Book Rating : 397/5 ( reviews)

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Book Synopsis Function Field Arithmetic by : Dinesh S. Thakur

Download or read book Function Field Arithmetic written by Dinesh S. Thakur. This book was released on 2004. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an exposition of function field arithmetic with emphasis on recent developments concerning Drinfeld modules, the arithmetic of special values of transcendental functions (such as zeta and gamma functions and their interpolations), diophantine approximation and related interesting open problems. While it covers many topics treated in 'Basic Structures of Function Field Arithmetic' by David Goss, it complements that book with the inclusion of recent developments as well as the treatment of new topics such as diophantine approximation, hypergeometric functions, modular forms, transcendence, automata and solitons. There is also new work on multizeta values and log-algebraicity. The author has included numerous worked-out examples. Many open problems, which can serve as good thesis problems, are discussed.

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.

The Arithmetic of Function Fields

2011-06-24 Mathematics
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Release : 2011-06-24
Genre : Mathematics
Kind : eBook
Book Rating : 154/5 ( reviews)

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Book Synopsis The Arithmetic of Function Fields by : David Goss

Download or read book The Arithmetic of Function Fields written by David Goss. This book was released on 2011-06-24. Available in PDF, EPUB and Kindle. Book excerpt: Thisseries is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.

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