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Title: Two dynamical perspectives on the randomness of the Mobius function
Authors: Peckner, Ryan Nathaniel
Advisors: Sarnak, Peter C
Contributors: Mathematics Department
Subjects: Mathematics
Issue Date: 2015
Publisher: Princeton, NJ : Princeton University
Abstract: Sarnak's approach to the Mobius randomness heuristic from the standpoint of dynamical systems is studied in two complementary settings. First, the Mobius function is realized in the context of symbolic dynamics, and we prove that its associated squarefree factor has a unique measure of maximal entropy. We then show that the Mobius function is linearly disjoint from all zero-entropy translations on homogeneous spaces of connected Lie groups, generalizing work of Vinogradov, Green-Tao, and Bourgain- Sarnak-Ziegler.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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