Mathematical Sciences: Problems in Analytic Number Theory

数学科学：解析数论问题

• 批准号: 9622753
• 负责人: Steven Gonek
• 金额: $ 6万
• 依托单位: University of Rochester
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 1999-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622753&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Analytic; Number

Gonek 9622753 Professor Gonek will study various problems concerning the distribution of zeros and the mean values of the Riemann zeta function. He hopes to show that certain analogues of the zeta function defined by Dirichlet series have a positive proportion of zeros off the critical strip. He also intends to study various moment problems for the zeta function. He will also study additive divisor problems and theorems of Barban-Davenport-Halberstam type. This project falls into the general area of number theory. Number theory is one of the oldest areas of mathematics and yet every generation returns to these problems again. Encryption and error correcting codes have been vastly improved as a direct consequence of recent research in number theory. ??

戈内克9622753 教授Gonek将研究有关零点的分布和黎曼zeta函数的平均值的各种问题。他希望表明，某些类似的zeta函数定义的狄利克雷级数有一个积极的比例零小康的关键地带。他还打算研究zeta函数的各种矩问题。他还将研究添加剂除数问题和定理的Barban-Davenport-Halberlane型。 这个项目福尔斯属于数论的一般领域。数论是数学中最古老的领域之一，然而每一代人都会再次回到这些问题。加密和纠错码已经得到了极大的改进，这是最近数论研究的直接结果。 ??