Lindelöf's Theorem
Let f(s) defined and analytic in a half-strip D={s:sigma_1<=R[s]<=sigma_2,I[s]>=t_0 0}. If |f|<=M on the boundary partialD of D and there is a constant A such that |f(sigma+it)|t^(-A) is bounded on D, then |f|<=M throughout D (Edwards 2001, p. 2001).
See also
Lindelöf's Catenary Theorem, Lindelöf HypothesisExplore with Wolfram|Alpha
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References
Edwards, H. M. Riemann's Zeta Function. New York: Dover, p. 184, 2001.Lindelöf, E. "Quelque remarques sur la croissance de la fonction zeta(s)." Bull. Sci. Math. 32, 341-356, 1908.Referenced on Wolfram|Alpha
Lindelöf's TheoremCite this as:
Weisstein, Eric W. "Lindelöf's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LindelofsTheorem.html