10 edition of **Algebraic curves over finite fields** found in the catalog.

- 70 Want to read
- 13 Currently reading

Published
**1991**
by Cambridge University Press in Cambridge [England], New York
.

Written in English

- Curves, Algebraic,
- Algebraic fields,
- Functions, Zeta

**Edition Notes**

Includes bibliographical references (p. 239-244) and index.

Statement | Carlos Moreno. |

Series | Cambridge tracts in mathematics ;, 97 |

Classifications | |
---|---|

LC Classifications | QA565 .M84 1990 |

The Physical Object | |

Pagination | ix, 246 p. : |

Number of Pages | 246 |

ID Numbers | |

Open Library | OL1861176M |

ISBN 10 | 052134252X |

LC Control Number | 90015032 |

Buy a cheap copy of Algebraic Curves over Finite Fields: book by Carlos Moreno. In this tract, Professor Moreno develops the theory of algebraic curves over finite fields, their zeta and L-functions, and, for the first time, the theory of Free shipping over $ "Goldschmidt brings readers, in a minimal number of pages, from first principles to a major landmark of 20th-century mathematics (which falls outside of Riemann surface theory!), namely, Weil’s Riemann hypothesis for curves over finite fields. An excellent stepping stone either to algebraic number theory or to abstract algebraic geometry."Brand: Springer-Verlag New York.

theory of algebraic curves from the viewpoint of modern algebraic geometry, but without excessive prerequisites. We have assumed that the reader is familiar with some basic properties of rings, ideals, and polynomials, such as is often covered in a one-semester course in mod-ern algebra; additional commutative algebra is developed in later File Size: KB. This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes. There are four main divisions in the book. The first is a brief exposition of basic concepts and facts of the theory of error-correcting codes (Part I). The second is a complete presentation of the theory of algebraic curves, especially the curves defined over finite fields (Part II). The.

2 1. INTRODUCTION In , Gerard van der Geer and Marcel van der Vlugt [32] started a table of N q(g) for g 50 and qa small power 2 or , this was embedded in a larger project of determining NCited by: 5. This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry.

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This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry.

The theory of algebraic curves over finite fields, their zeta and L-functions, and, for the first time, the theory of algebraic geometric Goppa codes on algebraic curves are developed in this text.

Electrical engineers as well as mathematics students will find the material of by: Rational points on algebraic curves over finite fields is a key topic for algebraic geometers and coding theorists. Here, the authors relate an important application of such curves, namely, to the construction of low-discrepancy sequences, needed for numerical methods in diverse by: "This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many.

Get this from a library. Algebraic curves over finite fields. [Carlos J Moreno] -- "In this Tract, Professor Moreno develops the theory of algebraic curves over finite fields, their zeta and L-functions, and, for the first time, the theory of algebraic geometric Goppa codes on.

This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and : $ Very useful both for research and in the classroom.

The main reason to use this book in a classroom is to prepare students for Algebraic curves over finite fields book research in the fields of finite geometries, curves in positive characteristic in a projective space, and curves over a finite field and their applications to coding theory.4/5(1).

Abstract. Algebraic curves over finite fields with many rational points have received a lot of attention in recent years. We present a survey of this subject covering both the case of fixed genus and the asymptotic by: 2.

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 by: This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, 4/5(1).

This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology.

This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes. There are four main divisions in the book.

The first is a brief exposition of basic concepts and facts of the theory of error-correcting codes (Part I). The second is a complete presentation of.

This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes. There are four main divisions in the book. The first is a brief exposition of basic concepts and facts of the theory of error-correcting codes (Part I).

Van Der Geer G. () Coding Theory and Algebraic Curves Over Finite Fields. In: Ciliberto C., Hirzebruch F., Miranda R., Teicher M. (eds) Applications of Algebraic Geometry to Coding Theory, Physics and Computation.

NATO Science Series (Series II: Mathematics, Physics and Chemistry), vol Springer, DordrechtCited by: 3. “Algebraic Curves over a Finite Field” is a rich, example-filled, comprehensive introduction to the subject.

As an easy-to-read introductory book that presents the general theory of algebraic curves over finite fields, it fills a large gap in the literature. Elliptic curves over finite fields are notably applied in cryptography and for the factorization of large integers.

These algorithms often make use of the group structure on the points of E. Algorithms that are applicable to general groups, for example the group of invertible elements in finite fields, F * q, can thus be applied to the group.

A course in Elliptic Curves. This note covers the following topics: Fermat’s method of descent, Plane curves, The degree of a morphism, Riemann-Roch space, Weierstrass equations, The group law, The invariant differential, Formal groups, Elliptic curves over local fields, Kummer Theory, Mordell-Weil, Dual isogenies and the Weil pairing, Galois cohomology, Descent by cyclic isogeny.

This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology.

Unlike other books, this one emphasizes the algebraic geometry rather. Answer to 1. is Silverman. Answer to 2. is yes.

Answers to 3. and 4. do not appear obviously in the chapter on elliptic curves over finite fields, where only generalities seem to be treated. $\endgroup$ – doktorkrampus Oct 29 '10 at This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes.

There are four main divisions in the book. The first is a brief exposition of basic concepts and facts of the theory of error-correcting codes (Part I). The second is a complete presentation of the theory of algebraic curves, especially the curves defined over finite fields (Part II).

Buy Algebraic Curves over Finite Fields: Error-correcting Codes and Exponential Sums (Cambridge Tracts in Mathematics) New Ed by Moreno, Carlos (ISBN: ) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders.4/5(1)."This book is a self-contained guide to the theory of algebraic curves over a finite field, one that leads readers to various recent results in this and related areas.

Personally I was attracted by the rich examples explained in this book."4/5(1).Algebraic function fields. The study of algebraic curves can be reduced to the study of irreducible algebraic curves: those curves that cannot be written as the union of two smaller curves.

Up to birational equivalence, the irreducible curves over a field F are categorically equivalent to algebraic function fields in one variable over F.