# The Lindelöf hypothesis for admissible sequences

Specialeforsvar: Line Lindholm Jensen

Titel: The Lindelöf hypothesis for admissible sequences

Abstract: We provide a general introduction to the Lindelöf hypothesis and show several equivalent formulations of the famous conjecture. In particular, we will see the connection to the zeroes of the zeta function, but most importantly we focus on the recent formulation made by Gonek, Graham and Lee. This new formulation leads to a generalization of the Lindelöf hypothesis as an estimate concerning the sums $$\sum_{\substack{n \in \mathcal{N}\\ n \leq x}}n^{-it},$$ for admissible sequences $\mathcal{N}$.
Supporting this new conjecture with several examples, we expect that a more general form of the classical conjecture may be true. As our main result, we show that for the sequence of prime numbers this new conjecture is equivalent to the Riemann hypothesis

Vejleder: Morten Risager
Censor:    Jacob Stordal Christiansen, Lund Universitet