摘要
三角积分零点实性问题源于对黎曼猜想的研究,利用历史分析和比较的方法,深入解读了波利亚在此方面的8篇文章,较为细致全面地揭示了波利亚的一些重要思想和方法.他的工作得益于胡尔维兹、延森、兰道、外尔等人的工作.他提出了研究三角积分零点实性的广义因子法和研究黎曼猜想的逼近方法.波利亚是系统研究三角积分零点实性问题最大贡献的数学家,其工作至今对许多数学家有重要影响.
The reality of the zeros of trigonometric integrals originates from the study of Riemann hypothesis.This paper deeply interprets P■lya’s eight articles on this aspect,and reveals some important thoughts and methods of G.P■lya in detail based on the original literature,historical analysis and method of the comparison.His work benefited from the work of hurwitz,Jensen,landau,wely.He proposed the generalized factor method and the approximate method for studying Riemann hypothesis.P■lya is a mathematician who has made the greatest contribution to the systematic study of the reality of the zeros of trigonometric integrals.His work now still has great influence on many mathematicians.
作者
王全来
Wang Quanlai(College of Computer and Information Engineering,Tianjin Normal University,Tianjin 300387,China)
出处
《纯粹数学与应用数学》
2019年第4期482-504,共23页
Pure and Applied Mathematics
基金
国家自然科学基金(11571276)
关键词
三角积分
零点实性
黎曼猜想
整函数
trigonometric integrals
the reality of the zeros
Riemann hypothesis
entire function
