The Selberg integral and a new pair-correlation function for the zeros of the Riemann zeta-function

2016/03/09 by Alessandro Zaccagnini, Zaccagnini, Alessandro
Mathematics · #11M26 11N05 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #math.NT #msc:11M26 #msc:11N05

paper · pdf · doi:10.48550/arxiv.1603.02952

Proceedings of the Third Italian Meeting in Number Theory, Pisa, September 2015. To appear in the "Rivista di Matematica dell'Universita` di Parma"

arxiv created 2016/03/09 · openalex publication_date 2016/03/09 · arxiv updated 2016/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The present paper is a report on joint work with Alessandro Languasco and Alberto Perelli on our recent investigations on the Selberg integral and its connections to Montgomery's pair-correlation function. We introduce a more general form of the Selberg integral and connect it to a new pair-correlation function, emphasising its relations to the distribution of prime numbers in short intervals.

Related

• Notes on Pair Correlation of Zeros and Prime Numbers
• Pair Correlation Estimates for the Zeros of the Zeta Function via Semidefinite Programming
• Correlations of sieve weights and distributions of zeros
• Pair correlation: Variations on a theme
• Pair Correlation Conjecture for the zeros of the Riemann zeta-function II: The Alternative Hypothesis