Distribution of multiplicative functions and other topics in analytic number theory

乘法函数的分布和解析数论中的其他主题

• 批准号: 435272-2013
• 负责人: Koukoulopoulos, Dimitrios
• 金额: $ 1.46万
• 依托单位: Université de Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=596655
• 关键词: Distribution; multiplicative; functions; other; topics

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.

乘法是主要的算术运算之一。理解这一简单操作的精细属性会带来令人惊讶的深刻问题。例如，素数是不能写成另外两个严格较小的整数的乘积的整数(整数)。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，是数学中最热门的问题之一。