Variants of the Mobius function

Thursday, September 21, 2017 - 8:30pm
MSB 312
William Banks (University of Missouri, Columbia)

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