2015/05/27 by Owen Barrett, F.W.K. Firk, Barrett, Owen +5
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1505.07481
openalex publication_date 2015/05/27 · openalex created_date 2022/09/25 · openalex updated_date 2026/07/28
The discovery of connections between the distribution of energy levels of\nheavy nuclei and spacings between prime numbers has been one of the most\nsurprising and fruitful observations in the twentieth century. The connection\nbetween the two areas was first observed through Montgomery's work on the pair\ncorrelation of zeros of the Riemann zeta function. As its generalizations and\nconsequences have motivated much of the following work, and to this day remains\none of the most important outstanding conjectures in the field, it occupies a\ncentral role in our discussion below. We describe some of the many techniques\nand results from the past sixty years, especially the important roles played by\nnumerical and experimental investigations, that led to the discovery of the\nconnections and progress towards understanding the behaviors. In our survey of\nthese two areas, we describe the common mathematics that explains the\nremarkable universality. We conclude with some thoughts on what might lie ahead\nin the pair correlation of zeros of the zeta function, and other similar\nquantities.\n