The hypothesis asks for growth smaller than every fixed positive power on the critical line. The implied constant may depend on the chosen exponent. The Riemann hypothesis implies the Lindelöf hypothesis through a smoothed explicit formula and strip convexity.
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The Lindelöf hypothesis is a conjecture in number theory, specifically related to the distribution of prime numbers and the Riemann zeta function. Proposed by the Swedish mathematician Ernst Lindelöf in 1908, it posits that the Riemann zeta function \(\zeta(s)\) has a certain bounded behavior for complex numbers \(s\) in the critical strip, where the real part of \(s\) is between 0 and 1.