Zero-free half-planes of the ζ-function via spaces of analytic functions.

In this article we introduce a general approach for deriving zero-free half-planes for the Riemann zeta function ζ by identifying topological vector spaces of analytic functions with specific properties. This approach is applied to weighted ℓ 2 spaces and the classical Hardy spaces H p (0 < p ≤ 2). As a consequence precise conditions are obtained for the existence of zero-free half planes for the ζ -function. [ABSTRACT FROM AUTHOR]