On fluctuations of Riemann's zeta zeros

• 成果类型: Article
• 署名作者: Kargin, V.
• 署名单位: University of Cambridge
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-012-0465-9
• 发表日期: 2013
• 页码: 575-604
• 关键词: eigenvalues

摘要

It is shown that the normalized fluctuations of Riemann's zeta zeros around their predicted locations follow the Gaussian law. It is also shown that fluctuations of two zeros,gamma k and gamma k+x, with x similar to (log k)(beta), beta > 0, for large k follow the two-variate Gaussian distribution with correlation (1 - beta)(+).