Statistics of the zeros of L-functions and arithmetic correlations

2016/07/12 by David J. Smith, Smith, D. J.
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1607.03297

openalex publication_date 2016/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This thesis determines some of the implications of non-universal and emergent universal statistics on arithmetic correlations and fluctuations of arithmetic functions, in particular correlations amongst prime numbers and the variance of the expected number of prime numbers over short intervals are generalised by associating these concepts to L-functions arising from number theoretic objects.

Citations

• Correlations between Periodic Orbits and their R?le in Spectral Statistics
• Zeros of principal L-functions and random matrix theory

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