Algebraic Curves over a Finite Field
eBook - PDF

Algebraic Curves over a Finite Field

J. W. P. Hirschfeld, Gabor Korchmaros, Fernando Torres

  1. 744 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Algebraic Curves over a Finite Field

J. W. P. Hirschfeld, Gabor Korchmaros, Fernando Torres

Book details
Table of contents
Citations

About This 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 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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Information

Year
2013
ISBN
9781400847419

Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. Dedication
  5. Contents
  6. Preface
  7. PART 1. GENERAL THEORY OF CURVES
  8. PART 2. CURVES OVER A FINITE FIELD
  9. PART 3. FURTHER DEVELOPMENTS
  10. Appendix A. Background on field theory and group theory
  11. Appendix B. Notation
  12. Bibliography
  13. Index
Citation styles for Algebraic Curves over a Finite Field

APA 6 Citation

Hirschfeld, J., Korchmáros, G., & Torres, F. (2013). Algebraic Curves over a Finite Field ([edition unavailable]). Princeton University Press. Retrieved from https://www.perlego.com/book/735791/algebraic-curves-over-a-finite-field-pdf (Original work published 2013)

Chicago Citation

Hirschfeld, J, G Korchmáros, and F Torres. (2013) 2013. Algebraic Curves over a Finite Field. [Edition unavailable]. Princeton University Press. https://www.perlego.com/book/735791/algebraic-curves-over-a-finite-field-pdf.

Harvard Citation

Hirschfeld, J., Korchmáros, G. and Torres, F. (2013) Algebraic Curves over a Finite Field. [edition unavailable]. Princeton University Press. Available at: https://www.perlego.com/book/735791/algebraic-curves-over-a-finite-field-pdf (Accessed: 14 October 2022).

MLA 7 Citation

Hirschfeld, J, G Korchmáros, and F Torres. Algebraic Curves over a Finite Field. [edition unavailable]. Princeton University Press, 2013. Web. 14 Oct. 2022.