Lindelöf hypothesis

Importance: Medium ✭✭

Author(s):

Subject:	Number Theory
	» Analytic Number Theory

Keywords:	Riemann Hypothesis
	zeta

Recomm. for undergrads: no

Posted	by:	porton
	on:	September 20th, 2010

Conjecture For any $\epsilon>0$

$\zeta\left(\frac12 + it\right) \mbox{ is }\mathcal{O}(t^\epsilon).$

Since $\epsilon$ can be replaced by a smaller value, we can also write the conjecture as, for any positive $\epsilon$ ,

$\zeta\left(\frac12 + it\right) \mbox{ is }o(t^\varepsilon).$

Accordingly Wikipedia this hypothesis is implied by Riemann hypothesis.

Bibliography

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