Implications of subconvexity bounds for the moments of zeta

TL;DR

This paper investigates how bounds on the moments of the Riemann zeta function relate to subconvexity bounds, using functional analysis to understand potential changes in the moments' behavior.

Contribution

It provides a new perspective on the relationship between moment bounds and subconvexity, characterizing possible transitions in their behavior.

Findings

Characterization of potential transitions in moment behavior

Implications for subconvexity bounds from moment bounds

Use of functional analysis in the right-half of the critical strip

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.