Primality Testing and Abelian Varieties Over Finite Fields

1. Front Matter

   Pages I-VII

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2. Introduction

   • Leonard M. Adleman, Ming-Deh A. Huang

   Pages 1-3

3. Acknowledgement

   • Leonard M. Adleman, Ming-Deh A. Huang

   Pages 4-4

4. Overview of the algorithm and the proof of the main theorem

   • Leonard M. Adleman, Ming-Deh A. Huang

   Pages 5-14

5. Reduction of main theorem to three propositions

   • Leonard M. Adleman, Ming-Deh A. Huang

   Pages 15-21

6. Proof of proposition 1

   • Leonard M. Adleman, Ming-Deh A. Huang

   Pages 21-109

7. Proof of proposition 2

   • Leonard M. Adleman, Ming-Deh A. Huang

   Pages 110-125

8. Proof of proposition 3

   • Leonard M. Adleman, Ming-Deh A. Huang

   Pages 126-136

9. Back Matter

   Pages 137-142

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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.

• Abelian Varieties
• Computational Complexity
• Number theory
• Prime
• Prime Numbers
• Prime number
• finite field
• combinatorics

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