Algorithms in Number Theory

这是一个更新项目，以调查计算 数论问题的复杂性。 除了提供 复杂性理论中未解决问题的数量 理论在随机数系统的设计中是有用的 生成、密码学和计算机代数。 的 调查分为三类： a）探索启发式算法的结果 扩展的黎曼猜想（Extended Riemann Hypothesis） B）数论算法的分析和设计， 特别注意有效的随机化 素数的算法，多项式的因式分解， 等 c）代数几何的应用（特别是理论 有限域上的变种）到构造词 技术.

This is a renewal project to investigate the compuational complexity of number-theoretic problems. Besides providing a number of unsolved problems in complexity theory, number theory is useful in the design of systems for random number generation, cryptography, and computer algebra. The investigations fall into three categories: a) Exploration of the algorithmic consequences of heuristic assumptions such as the Extended Riemann Hypothesis. b) Analysis and design of number-theoretic algorithms, with special attention being paid to efficient randomized algorithms for primality, factorization of polynomials, etc. c) Applications of algebraic geometry (especially the theory of varieties over finite fields) to constructives techniques.