L-functions and Multiplicative Number Theory

研究者和他的同事们研究了l函数解析理论和乘法函数均值中的各种问题。特别是研究者的目标是提高对l函数的零分布的理解，它们在特殊值下的行为，以及临界带中极值的大小。这个项目的第二个主要目的是描述乘法函数的可能均值的谱，这些函数在素数处的值被限制在单位圆盘的特殊子集中。研究者与Granville合作，打算进一步发展这样的均值和一组积分方程的解之间的密切联系。这个项目涉及乘法数论领域的问题。这个领域的一个基本问题是理解黎曼ζ函数和其他l函数的零点。这些函数编码了很多关于素数和其他算术对象的信息。除了数学家的内在兴趣之外，从这些问题中产生的想法已经在计算机科学，密码学和编码理论中得到了应用。

The investigator and his colleagues study various problems inthe analytic theory of L-functions and mean values of multiplicativefunctions. In particular the investigator aims for an improvedunderstanding of the distribution of zeros of L-functions,their behaviour at special values, and the size of extreme valuesin the critical strip. The second main aim of this project isto describe the spectrum of possible mean-values of multiplicativefunctions whose values at primes are constrained to lie in specialsubsets of the unit disc. The investigator, in collaborationwith Granville, intends to develop further the close connection betweensuch mean values and solutions to a family of integral equations.This project concerns problems in the area of multiplicativenumber theory. A fundamental problem in this area is to understandthe zeros of the Riemann zeta function and other L-functions. Thesefunctions encode much information about prime numbers, andother arithmetic objects. Besides being of intrinsic interest tomathematicians, ideas emerging from these problems have found usein computer science, cryptography and coding theory.