Non-vanishing of Dirichlet series without Euler products

Abstract

We give a new proof that the Riemann zeta function is nonzero in the half-plane $\{s\in{\mathbb C}:\sigma>1\}$. A novel feature of this proof is that it makes no use of the Euler product for $\zeta(s)$.Comment: 13 pages; some minor edits of the previous versio