# Latest well-known outcome on Lindelöf theory

The Phragmen-Lindelöf theorem offers an effect of the Riemann theory, viz, the Lindelöf hypothesis. Thus this is weak than Riemann theory; yet it is still taken into consideration that also an evidence of this weak outcome will certainly be an innovation.

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What is the toughest well-known outcome yet on the Lindelöf theory?

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Answers: 1

The ideal outcome presently recognized along these lines, as a result of Hermann Weyl, is that $$|\zeta(\frac{1}{2}+it)|=\mathcal{O}(\tau^{16+\epsilon})$$ for any kind of $\epsilon > 0$ as $\tau \to \infty$.

You can refer even more concerning this on : http://www.openquestions.com/oq-ma014.htm

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