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Date: 14-8-2019
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Date: 18-8-2018
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Let be the least upper bound of the numbers such that is bounded as , where is the Riemann zeta function. Then the Lindelöf hypothesis states that is the simplest function that is zero for and for .
The Lindelöf hypothesis is equivalent to the hypothesis that (Edwards 2001, p. 186).
Backlund (1918-1919) proved that the Lindelöf hypothesis is equivalent to the statement that for every , the number of roots in the rectangle grows less rapidly than as (Edwards 2001, p. 188).
REFERENCES:
Backlund, R. "Über die Beziehung zwischen Anwachsen und Nullstellen der Zeta-Funktion." Ofversigt Finka Vetensk. Soc. 61, No. 9, 1918-1919.
Edwards, H. M. Riemann's Zeta Function. New York: Dover, 2001.
Lindelöf, E. "Quelque remarques sur la croissance de la fonction ." Bull. Sci. Math. 32, 341-356, 1908.
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