Ethan Ackelsberg: The Daboussi—Kátai Orthogonality Criterion

Friday, April 22, 4-5 pm, MW 154

Abstract: I will discuss a criterion due to Daboussi and Kátai for checking that a bounded sequence a : ℕ → ℂ is asymptotically orthogonal to multiplicative functions (such as the Möbius or Liouville function). This allows for alternative proofs of (and generalizations of) the orthogonality results of Davenport and Green and Tao and provides motivation for a result about the structure of multiplicative functions due to Bergelson, Kułaga-Przymus, Lemańczyk, and Richter.

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