Phragmén–Lindelöf principle
= Phragmén–Lindelöf principle
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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.