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 Hypothesis

Explore with Wolfram|Alpha


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 Theorem

Cite this as:

Weisstein, Eric W. "Lindelöf's Theorem." From MathWorld--A Wolfram Web Resource.

Subject classifications