2004/12/16 by D. A. Goldston, Goldston, D. A.
Mathematics · Physics and Astronomy · #11N05 #11N37 #Advanced Mathematical Theories and Applications #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Number Theory (math.NT) #math.NT #msc:11N05 #msc:11N37
paper · pdf · doi:10.48550/arxiv.math/0412313
arxiv created 2004/12/16 · openalex publication_date 2004/12/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
These notes are based on my four lectures given at the Newton Institute in April 2004 during the Recent Perspectives in Random Matrix Theory and Number Theory Workshop. Their purpose is to introduce the reader to the analytic number theory necessary to understand Montgomery's work on the pair correlation of the zeros of the Riemann zeta-function and subsequent work on how this relates to prime numbers. A very brief introduction to Selberg's work on the moments of S(T) is also given.