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 $\zeta(s)$.
Non-vanishing of Dirichlet series with periodic coefficients
A segment of Euler product associated to a certain Dirichlet series
On a conjecture of Erdös and certain Dirichlet series
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