Mathematical Sciences: Topics in Analytic and Algorithmic Number Theory

该奖项支持佐治亚大学的卡尔·波梅兰斯和赫尔穆特·迈尔教授在数论方面的研究。波梅兰斯博士的研究将集中在整数因式分解算法，以及研究没有大素数因子的整数在算术级数中的分布以及整数的除数序列的性质。迈尔博士的项目是继续他关于短区间素数分布的不规则性的工作，并研究割圆多项式的系数。除计数外，数论是数学中最古老的分支，它研究整体数的性质。在现代，数论中的问题提供了在纯代数、分析和几何领域创造新数学的动力；一些最新和最令人惊讶的数论应用出现在理论计算机科学和编码理论中。

This award supports the research in number theory of Professors Carl Pomerance and Helmut Maier of the University of Georgia. Dr. Pomerance's research will center on integer factoring algorithms and studies of the distribution in arithmetic progressions of integers with no large prime factor as well as properties of the sequence of divisors of an integer. Dr Maier's project is to continue his work on irregularities in the distribution of prime numbers in short intervals, and also to study the coefficients of the cyclotomic polynomials. Except for counting, number theory, which is the study of the properties of the whole numbers, is the oldest branch of mathematics. In modern days, problems in number theory have furnished the driving force to creation of new mathematics in the fields of pure algebra, analysis, and geometry; some of the most recent and most astonishing applications of number theory have appeared in theoretical computer science and coding theory.