Regularized products of Gauss and Eisenstein integers and primes
Number Theory
2025-10-29 v1 Mathematical Physics
math.MP
Abstract
We provide heuristic computations \`a la Euler of the regularized infinite products of Gauss and Eisenstein integers and primes. Our approach, yielding explicit expressions, is inspired by the work by Mu\~noz Garc\'ia and P\'erez-Marco, who evaluated the product of all natural primes to .
Cite
@article{arxiv.2510.24271,
title = {Regularized products of Gauss and Eisenstein integers and primes},
author = {P. L. Krapivsky and J. M. Luck},
journal= {arXiv preprint arXiv:2510.24271},
year = {2025}
}
Comments
11 pages. 25 references. Comments welcome