The Riemann Hypothesis In Algebraic Function Fields Over A Finite Constants Field
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The Riemann Hypothesis In Algebraic Function Fields Over A Finite Constants Field
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Author : Helmut Hasse
language : en
Publisher:
Release Date : 1968
The Riemann Hypothesis In Algebraic Function Fields Over A Finite Constants Field written by Helmut Hasse and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Algebraic fields categories.
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.
The Riemann Hypothesis In Algebraic Function Fields Over A Finite Constants Field
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Author : Helmut Hasse
language : en
Publisher:
Release Date : 1968
The Riemann Hypothesis In Algebraic Function Fields Over A Finite Constants Field written by Helmut Hasse and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Algebraic fields categories.
Rational Points On Curves Over Finite Fields
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Author : Harald Niederreiter
language : en
Publisher: Cambridge University Press
Release Date : 2001-06-14
Rational Points On Curves Over Finite Fields written by Harald Niederreiter and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-14 with Computers categories.
Ever since the seminal work of Goppa on algebraic-geometry codes, rational points on algebraic curves over finite fields have been an important research topic for algebraic geometers and coding theorists. The focus in this application of algebraic geometry to coding theory is on algebraic curves over finite fields with many rational points (relative to the genus). Recently, the authors discovered another important application of such curves, namely to the construction of low-discrepancy sequences. These sequences are needed for numerical methods in areas as diverse as computational physics and mathematical finance. This has given additional impetus to the theory of, and the search for, algebraic curves over finite fields with many rational points. This book aims to sum up the theoretical work on algebraic curves over finite fields with many rational points and to discuss the applications of such curves to algebraic coding theory and the construction of low-discrepancy sequences.
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 Riemann Hypothesis For Algebraic Function Fields Of One Variable Over A Finite Constant Field
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Author : Kok Leang Chin
language : en
Publisher:
Release Date : 1978
The Riemann Hypothesis For Algebraic Function Fields Of One Variable Over A Finite Constant Field written by Kok Leang Chin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Algebraic fields categories.
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.
The Riemann Hypothesis For Function Fields
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Author : Machiel Van Frankenhuysen
language : en
Publisher: Cambridge University Press
Release Date : 2014-01-09
The Riemann Hypothesis For Function Fields written by Machiel Van Frankenhuysen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-09 with Mathematics categories.
An exposition of the theory of curves over a finite field, and connections to the Riemann Hypothesis for function fields.
Algebraic Curves Over Finite Fields
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Author : Carlos Moreno
language : en
Publisher: Cambridge University Press
Release Date : 1993-10-14
Algebraic Curves Over Finite Fields written by Carlos Moreno and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-14 with Mathematics categories.
Develops the theory of algebraic curves over finite fields, their zeta and L-functions and the theory of algebraic geometric Goppa codes.
The Riemann Hypothesis In Characteristic P In Historical Perspective
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Author : Peter Roquette
language : en
Publisher: Springer
Release Date : 2018-09-28
The Riemann Hypothesis In Characteristic P In Historical Perspective written by Peter Roquette and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-28 with Mathematics categories.
This book tells the story of the Riemann hypothesis for function fields (or curves) starting with Artin's 1921 thesis, covering Hasse's work in the 1930s on elliptic fields and more, and concluding with Weil's final proof in 1948. The main sources are letters which were exchanged among the protagonists during that time, found in various archives, mostly the University Library in Göttingen. The aim is to show how the ideas formed, and how the proper notions and proofs were found, providing a particularly well-documented illustration of how mathematics develops in general. The book is written for mathematicians, but it does not require any special knowledge of particular mathematical fields.