Year: 2025
Type: preprint
Abstract: Assuming the Riemann Hypothesis, we extend Montgomery's pair correlation method to study the distribution of differences between sums $γ_1+γ_2$ of two ordinates of nontrivial zeros of the Riemann zeta function. For the associated pair correlation function we prove that $G_2(α,T)=\{\log T/T^{2α}+4α^3/(3T^α)\} \{1+O(1/\log\log T)\}$ uniformly for $0\leα\le 2/3-2\log\log T/\log T$. In contrast with the conjectured GUE statistics of the ordinates themselves, this result points to an absence of level repulsion among sums of two ordinates, the two-point correlation function of the sums being identically one, as for a Poisson process.
Source: arXiv (Cornell University)
Author: Banks, William D.
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6966788771
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