From Gauss to G-del, mathematicians have sought an efficient
algorithm to distinguish prime numbers from composite numbers. This
book presents a random polynomial time algorithm for the problem.
The methods used are from arithmetic algebraic geometry, algebraic
number theory and analyticnumber theory. In particular, the theory
of two dimensional Abelian varieties over finite fields is
developed. The book will be of interest to both researchers and
graduate students in number theory and theoretical computer
science.
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