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: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=694457
• 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分析数论的替代方法，这是自黎曼1859年的回忆录以来的第一个连贯的计划。他现在可以定量地和定性地反驳所有经典结果，为众所周知的困难结果提供更简单的证明（例如林尼克定理和Hoheisel定理），并取得经典方法似乎无法取得的进展。现在，首席研究员希望了解均值的存在性并对其进行评估，找到如何积分三重积（以表明短间隔内存在素数），找到高阶消去，研究高权重l函数，发展与加性组合学和筛分的联系，并利用弥散方法。