Mathematical Sciences: Problems in Analytic Number Theory

9622753 Gonek教授将研究有关Riemann Zeta函数的零点分布和平均值的各种问题。他希望证明由狄利克莱级数定义的某些Zeta函数的类似物在临界带上有正比例的零点。他还打算研究Zeta函数的各种矩问题。他还将研究加性因子问题和Barban-Davenport-Halberstam类型的定理。这个项目属于数论的一般领域。数论是最古老的数学领域之一，然而每一代人都会再次回到这些问题上来。作为最近数论研究的直接结果，加密和纠错码已经得到了极大的改进。?？

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. ??