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Thursday, November 30, 2017

**Abstract:** This talk explores the question: To what extent does the Euler product expansion of the Riemann zeta function account for the non-vanishing of the Riemann zeta function in the half-plane $\{\Re(s)>1\}$? We exhibit a family of Dirichlet series that are closely related to the Riemann zeta function and are nonzero in $\{\Re(s)>1\}$, but do not possess an Euler product.