The Higher Rank Selberg Sieve and Applications

高阶塞尔伯格筛及其应用

• 批准号: RGPIN-2015-03957
• 负责人: Murty, Ram
• 金额: $ 2.99万
• 依托单位: Queen's University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=589496
• 关键词: Higher; Rank; Selberg; Sieve; Applications

In 1947, Atle Selberg discovered a new method in sieve theory which revolutionized the subject.  This method is now called the Selberg sieve and has been used in a spectrum of applications ranging from the classical twin prime problem to more sophisticated questions of counting points on algebraic varieties.  Recently, a special case of a "higher rank'' version of the Selberg sieve was applied by Maynard and Tao (independently) to improve and simplify upon Zhang's ground breaking work regarding infinitely many bounded gaps between consecutive prime numbers.  In joint work with my doctoral student,

1947年，Atle Selberg在筛法中发现了一种新的方法，彻底改变了筛法。这种方法现在被称为Selberg筛法，并已被用于从经典的孪生素数问题到代数簇上计数点的更复杂问题的一系列应用中。最近，梅纳德和陶应用了塞尔伯格筛的“高阶”版本的一个特例（独立）为了改进和简化张的开创性工作，关于连续素数之间的无限多个有界间隔。在与我的博士生的联合工作中，