Some notes on Euler products

TL;DR

This paper discusses the convergence properties of Euler products, emphasizing how the zeros of the Riemann zeta function serve as universal singularities affecting their behavior.

Contribution

It provides insights into the convergence phenomena of Euler products and the role of zeta zeros as universal singularities.

Findings

Zeta zeros are universal singularities of certain Euler products

Convergence behavior is influenced by the distribution of zeta zeros

Provides a deeper understanding of Euler product singularities

Abstract

We focus on a well-known convergence phenomenon, the fact that the $\zeta$ zeros are the universal singularities of certain Euler products.