A note on the distribution of clusters and deserts of prime numbers

Abstract:

We consider the distribution of values of weighted sums of the von Mangoldt arithmetical function. Using a formula for the distribution of values of trigonometric polynomials, we are able to present evidence supporting the claim that these weighted sums follow a distribution with a normal-like behavior.

Keywords: Primes in short intervals||Riemann zeta function||Explicit formulas

Journal: Indagationes Mathematicae

ISSN: 1872-6100

Year: 2025

Volume: 36

Number: 5

Pages: 1276-1287

Revision: 1

URL: https://www.sciencedirect.com/science/article/pii/S0019357725000266

DOI: 10.1016/j.indag.2025.03.007