Number Theory

数论

• 批准号: CRC-2015-00021
• 负责人: Granville, Andrew
• 金额: $ 14.57万
• 依托单位: Université de Montréal
• 依托单位国家: 加拿大
• 项目类别: Canada Research Chairs
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=729563
• 关键词: Number; Theory

The principal investigator is developing an alternative approach to analytic number theory, the first coherent program since Riemann's 1859 memoir. He can now reprove all classical results, quantitatively and qualitatively, providing simpler proofs of notoriously difficult results (E.g Theorems of Linnik and Hoheisel), and making advances that seemed inaccessible to classical methods. Now the principal investigator wishes to understand the existence of, and evaluate, mean values, find how to integrate triple products (to show there are primes in short intervals), find higher order cancelation, study higher weight L-functions, develop links to additive combinatorics and to the sieve, and exploit the dispersion method.

首席研究员正在开发一种替代解析数论的方法，这是自1859年里曼的回忆录以来的第一个连贯的程序。他现在可以在定量和定性上反驳所有经典结果，为臭名昭著的困难结果(例如林尼克和霍海塞尔定理)提供更简单的证明，并取得经典方法似乎无法获得的进展。现在主要的研究人员希望了解平均值的存在和评估，找到如何积分三重积(以证明在短区间内存在素数)，寻找高阶抵消，研究更高权重的L函数，发展到加性组合学和筛子的联系，并开发离散方法。