Algebraic curves over finite fields

By:

Moreno, Carlos

Series: Cambridge tracts in mathematics, no. 97Publication details: Cambridge University Press, 1993. Cambridge:Description: ix, 246p.; pbk; 24cmISBN:

9780521459013

Subject(s):

DDC classification:

516.352 MOR

Summary: 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. https://www.cambridge.org/core/books/algebraic-curves-over-finite-fields/5ADBB7158A73778E8AB82769A2ED5AE5#fndtn-information

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar	General	516.352 MOR (Browse shelf(Opens below))	1	Available		031775

Includes index and references

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.

https://www.cambridge.org/core/books/algebraic-curves-over-finite-fields/5ADBB7158A73778E8AB82769A2ED5AE5#fndtn-information

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