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The study in hand deals with a conjecture of Sarnak from 2010 about the orthogonality of sequences induced by deterministic dynamical systems to the Möbius function. Its main results are the ergodic theorem with Möbius weights, which is a measure theoretic (weaker) version of Sarnak´s conjecture, and the already assured validity of Sarnak´s conjecture in special cases, where we have exemplarily chosen the Thue-Morse shift and skew product extensions of rational rotations on the circle et al.

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Wabnitz, Paul
Paul Wabnitz was born in 1987 in Spremberg in the east of Germany. After School, in 2008 he attended the University of Leipzig to study Japanology and Philosophy but changed to Mathematics in 2010. He finished with a diploma in 2016. The work in hand is a corrected version of his diploma thesis.

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