Year: 2026
Type: article
Abstract: We provide a formula for the logarithmic density of the set of positive real numbers on which two prime counting functions $ψ(x;q,a)$ and $ψ(x;q,b)$ are simultaneously larger than their asymptotic main terms, as well as a method for calculating the numerical values of such densities with rigorously bounded errors. We apply these formulas to the pairwise races in the case $q=11$, determining which pairs of residues $a$ and $b$ are more or less correlated in this way. The outcomes when $q=11$ provide a deeper mathematical illumination of the "mirror image" and "cyclic ordering" phenomena observed by Bays and Hudson.
Source: Experimental Mathematics
Authors: Kübra Benli, Greg Martin, Paul Péringuey
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414976597
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