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arXiv · 2311.13441

On convergence of points to limiting processes, with an application to zeta zeros

Juan Arias de Reyna·Brad Rodgers
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Abstract

This paper considers sequences of points on the real line which have been randomly translated, and provides conditions under which various notions of convergence to a limiting point process are equivalent. In particular we consider convergence in correlation, convergence in distribution, and convergence of spacings between points. We also prove a simple Tauberian theorem regarding rescaled correlations. The results are applied to zeros of the Riemann zeta-function to show that several ways to state the GUE Hypothesis are equivalent. The proof relies on a moment bound of A. Fujii.

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Juan Arias de Reyna, Brad Rodgers. 2023-11-22. On convergence of points to limiting processes, with an application to zeta zeros. https://doi.org/10.1016/j.exmath.2024.125588

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