Algebraic curves over finite fields
著者
書誌事項
Algebraic curves over finite fields
（Cambridge tracts in mathematics, 97）
Cambridge University Press, 1993
1st pbk. ed
- : pbk
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注記
Bibliography: p. 239-244
Includes index
内容説明・目次
内容説明
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 algebraic curves. Amongst the applications considered are: the problem of counting the number of solutions of equations over finite fields; Bombieri's proof of the Reimann hypothesis for function fields, with consequences for the estimation of exponential sums in one variable; Goppa's theory of error-correcting codes constructed from linear systems on algebraic curves. There is also a new proof of the Tsfasman-Vladut-Zink theorem. The prerequisites needed to follow this book are few, and it can be used for graduate courses for mathematics students. Electrical engineers who need to understand the modern developments in the theory of error-correcting codes will also benefit from studying this work.
目次
- 1. Algebraic curves and function fields
- 2. The Riemann-Roch theorem
- 3. Zeta functions
- 4. Applications to exponential sums and zeta functions
- 5. Applications to coding theory
- Bibliography.
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