Regularized products of Gauss and Eisenstein integers and primes

Abstract

We provide heuristic computations à 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 Muñoz García and Pérez-Marco, who evaluated the product of all natural primes to $4{\pi }^2$.

11 pages. 25 references. Superseded by arXiv:2606.24536