Implications of subconvexity bounds for the moments of zeta

Abstract

It is well-known that upper bounds for moments of the Riemann zeta function $\zeta (s)$ have implications for subconvexity bounds. In this paper we explore some implications in the opposite direction using functional analysis in the right-half of the critical strip. The main results characterise potential transitions in the behaviour of the moments.

arXiv comment17 pages