TY  - BOOK
AU  - Moreno, Carlos J.
TI  - Algebraic curves over finite fiedls
SN  - 9781108732185
U1  - 516.352 MOR-C 
PY  - 2019///
CY  - India
PB  - Cambridge University Press
KW  - Algebraic fields
KW  - Curves, Algebraic
KW  - Functions, Zeta
N1  - 	
"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 Riemann 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
ER  -