Zeros of L-functions, and multiplicative and combinatorial number theory

L 函数的零点以及乘法和组合数论

• 批准号: 250190-2011
• 负责人: Martin, Greg
• 金额: $ 1.09万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=508592
• 关键词: Zeros; functions; multiplicative; combinatorial; number

Number theory is one of the most ancient fields of pure mathematics, often having unexpected application to the real world (such as cryptography and acoustics) as well as other fields of math. Analytic number theory revolves around the single central theme of using the techniques of analysis (such as calculus and complex numbers) to establish information about numbers (such as prime numbers and special sequences). My research involves three aspects of this central theme: combinatorial number theory, multiplicative groups in modular arithmetic, and zeros of L-functions.

数论是纯数学中最古老的领域之一，经常有意想不到的应用到真实的世界（如密码学和声学）以及其他数学领域。解析数论围绕着一个单一的中心主题，即使用分析技术（如微积分和复数）来建立有关数字的信息（如素数和特殊序列）。我的研究涉及这一中心主题的三个方面：组合数论，乘法组模算术，和零的L-函数。