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The Arithmetic Of Function Fields

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Basic Structures Of Function Field Arithmetic

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Author : David Goss
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Basic Structures Of Function Field Arithmetic written by David Goss 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 2012-12-06 with Mathematics categories.

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

Function Field Arithmetic

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Author : Dinesh S. Thakur
language : en
Publisher: World Scientific
Release Date : 2004

Function Field Arithmetic written by Dinesh S. Thakur and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

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.

Basic Structures Of Function Field Arithmetic

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Author : David Goss
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-11-18

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.

Number Theory In Function Fields

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Author : Michael Rosen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18

Number Theory In Function Fields written by Michael Rosen 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 2013-04-18 with Mathematics categories.

Elementary number theory is concerned with the arithmetic properties of the ring of integers, Z, and its field of fractions, the rational numbers, Q. Early on in the development of the subject it was noticed that Z has many properties in common with A = IF[T], the ring of polynomials over a finite field. Both rings are principal ideal domains, both have the property that the residue class ring of any non-zero ideal is finite, both rings have infinitely many prime elements, and both rings have finitely many units. Thus, one is led to suspect that many results which hold for Z have analogues of the ring A. This is indeed the case. The first four chapters of this book are devoted to illustrating this by presenting, for example, analogues of the little theorems of Fermat and Euler, Wilson's theorem, quadratic (and higher) reciprocity, the prime number theorem, and Dirichlet's theorem on primes in an arithmetic progression. All these results have been known for a long time, but it is hard to locate any exposition of them outside of the original papers. Algebraic number theory arises from elementary number theory by con sidering finite algebraic extensions K of Q, which are called algebraic num ber fields, and investigating properties of the ring of algebraic integers OK C K, defined as the integral closure of Z in K.

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.

The Arithmetic Of Function Fields

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Author : David Goss
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-24

The Arithmetic Of Function Fields written by David Goss and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-24 with Mathematics categories.

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.

Number Fields And Function Fields Two Parallel Worlds

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Author : Gerard van der Geer
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-09-14

Number Fields And Function Fields Two Parallel Worlds written by Gerard van der Geer 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 2005-09-14 with Mathematics categories.

Invited articles by leading researchers explore various aspects of the parallel worlds of function fields and number fields Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives Aimed at graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections

Advanced Topics In The Arithmetic Of Elliptic Curves

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Author : Joseph H. Silverman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Advanced Topics In The Arithmetic Of Elliptic Curves written by Joseph H. Silverman 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 2013-12-01 with Mathematics categories.

In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.

The Arithmetic Of Function Fields

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