Distribution of multiplicative functions and other topics in analytic number theory

乘法是算术运算中的主要运算之一。理解这个简单操作的精细性质会导致令人惊讶的深刻问题。例如，质数是整数（整数），不能写成两个其他严格较小的整数的乘积。所以2，3，5，7，11，...都是质数这些特殊的整数是乘法的“积木”，因为任何整数都可以写成素数的乘积。了解素数在所有整数的集合中的分布，以及在整数的其他特殊子集中的分布，是数学中最受关注的问题之一。

Multiplication is one of the main arithmetic operations. Understanding fine properties of this simple operation leads to surprisingly deep questions. For example, the prime numbers are integers (whole numbers) that cannot be written as product of two other, strictly smaller integers. So 2, 3, 5, 7, 11, ... are prime numbers. These special integers are the 'building blocks' of multiplication, since any integer can be written as the product of prime numbers. Understanding the distribution of prime numbers among the set of all integers, as well as among other special subsets of the integers, is one of the most sought questions in mathematics.