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Algebraic Curves over Finite Fields

Algebraic Curves over Finite Fields

£40.99

Part of Cambridge Tracts in Mathematics

  • Date Published: October 1993
  • availability: Available
  • format: Paperback
  • isbn: 9780521459013

£ 40.99
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  • 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.

    • Presents the underlying algebra of error-correcting codes
    • Subject matter is completely up-to-date
    • The first ever exposition of the theory of algebraic geometric Goppa codes on algebraic curves
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    ' … a careful and comprehensive guide to some of the most fascinating of plasma processes, a treatment that is both thorough and up-to-date.' The Observatory

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    Product details

    • Date Published: October 1993
    • format: Paperback
    • isbn: 9780521459013
    • length: 260 pages
    • dimensions: 229 x 152 x 15 mm
    • weight: 0.39kg
    • availability: Available
  • Table of Contents

    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.

  • Author

    Carlos Moreno, City University of New York

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