Phragmén–Lindelöf principle

A maximum-modulus extension for unbounded domains with suitable growth restrictions. In its polynomial-growth vertical-strip form, bounds $|F(a+it)|\ll (1+|t|{)}^u$ and $|F(b+it)|\ll (1+|t|{)}^v$ for a holomorphic function imply the interpolated exponent $((b-\sigma )u+(\sigma -a)v)/(b-a)$. It is the strip-convexity tool used to move subpower zeta bounds to the right of the critical line back onto that line.