# Algebraic Curves over a Finite Field (Princeton Series in Applied Mathematics)

## J. W.P. Hirschfeld; G. Korchmįros; F. Torres

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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, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves.

The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stöhr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students.

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"Very useful both for research and in the classroom. The main reason to use this book in a classroom is to prepare students for new 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. I think researchers will quote it for a long time."--Edoardo Ballico, University of Trento

"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."--Masaaki Homma, Kanagawa University

J.W.P. Hirschfeld is professor emeritus of mathematics at the University of Sussex. His books include Projective Geometries over Finite Fields. G. Korchmáros is professor of mathematics at the University of Basilicata in Italy. F. Torres is professor of mathematics at the University of Campinas in Brazil.

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

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## 1.Algebraic Curves over a Finite Field

Editore: Princeton University Press (2008)
ISBN 10: 0691096791 ISBN 13: 9780691096797
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Descrizione libro Princeton University Press, 2008. HRD. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria WP-9780691096797

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## 2.Algebraic Curves Over a Finite Field (Hardback)

Editore: Princeton University Press, United States (2008)
ISBN 10: 0691096791 ISBN 13: 9780691096797
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Descrizione libro Princeton University Press, United States, 2008. Hardback. Condizione libro: New. Language: English . Brand New Book. 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 than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stohr and Voloch.The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students. Codice libro della libreria AAH9780691096797

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## 3.Algebraic Curves over a Finite Field (Hardback)

Editore: Princeton University Press, United States (2008)
ISBN 10: 0691096791 ISBN 13: 9780691096797
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Descrizione libro Princeton University Press, United States, 2008. Hardback. Condizione libro: New. Language: English . Brand New Book. 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 than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stohr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students. Codice libro della libreria AAH9780691096797

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## 4.Algebraic Curves over a Finite Field (Princeton Series in Applied Mathematics)

Editore: Princeton University Press (2008)
ISBN 10: 0691096791 ISBN 13: 9780691096797
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Descrizione libro Princeton University Press, 2008. Hardcover. Condizione libro: New. Codice libro della libreria DADAX0691096791

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## 5.Algebraic Curves over a Finite Field

Editore: Princeton University Press (2008)
ISBN 10: 0691096791 ISBN 13: 9780691096797
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Descrizione libro Princeton University Press, 2008. HRD. Condizione libro: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria IP-9780691096797

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## 6.Algebraic Curves Over a Finite Field

Editore: Princeton University Press
ISBN 10: 0691096791 ISBN 13: 9780691096797
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Descrizione libro Princeton University Press. Hardback. Condizione libro: new. BRAND NEW, Algebraic Curves Over a Finite Field, J. W. P. Hirschfeld, G. Korchmaros, F. Torres, 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 than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stohr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students. Codice libro della libreria B9780691096797

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## 7.Algebraic Curves over a Finite Field (Princeton Series in Applied Mathematics)

Editore: Princeton University Press (2008)
ISBN 10: 0691096791 ISBN 13: 9780691096797
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Descrizione libro Princeton University Press, 2008. Hardcover. Condizione libro: New. Codice libro della libreria INGM9780691096797

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## 8.Algebraic Curves Over a Finite Field

Editore: Princeton University Press (2008)
ISBN 10: 0691096791 ISBN 13: 9780691096797
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Descrizione libro Princeton University Press, 2008. HRD. Condizione libro: New. New Book. Delivered from our US warehouse in 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND.Established seller since 2000. Codice libro della libreria IP-9780691096797

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## 9.Algebraic Curves over a Finite Field (Hardback)

Editore: Princeton University Press, United States (2008)
ISBN 10: 0691096791 ISBN 13: 9780691096797
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Descrizione libro Princeton University Press, United States, 2008. Hardback. Condizione libro: New. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. 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 than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stohr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students. Codice libro della libreria BTE9780691096797

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## 10.Algebraic Curves over a Finite Field (Princeton Series in Applied Mathematics)

Editore: Princeton University Press (2017)
ISBN 10: 0691096791 ISBN 13: 9780691096797
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Descrizione libro Princeton University Press, 2017. Hardcover. Condizione libro: New. Never used! This item is printed on demand. Codice libro della libreria P110691096791

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