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Benford's Law in the ring $\mathbb{Z}(\sqrt{D})$
Christine Patterson, Marion Scheepers
https://arxiv.org/abs/2402.10864 https://a…

Benford's Law in the ring $\mathbb{Z}(\sqrt{D})$
For $D$ a natural number that is not a perfect square and for $k$ a non-zero integer, consider the subset $\mathbb{Z}_k(\sqrt{D})$ of the quadratic integer ring $\mathbb{Z}(\sqrt{D})$ consisting of elements $x+y\sqrt{D}$ for which $x^2 - Dy^2 = k$ . For each $k$ such that the set $\mathbb{Z}_k(\sqrt{D})$ is nonempty, $\mathbb{Z}_k(\sqrt{D})$ has a natural arrangement into a sequence for which the corresponding sequence of integers $x$, as well as the corresponding sequence of integers $y$, are …

This https://arxiv.org/abs/2401.10609 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

First Digit Distributions of Gamma-Ray Bursts
The occurrence of the first significant digits from real world sources is usually not equally distributed, but is consistent with a logarithmic distribution instead, known as Benford's law. In this work, we perform a comprehensive investigation on the first digit distributions of the duration, fluence, and energy flux of gamma-ray bursts (GRBs) for the first time. For a complete GRB sample detected by the Fermi satellite, we find that the first digits of the duration and fluence adhere to Benfo…