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An application of the horocyclic flow to probabilistic number theory

Albert Artiles, University of Washington
Thursday, May 26, 2022 - 12:30pm to 1:30pm
RAI 116

Abstract: Consider the following question: Fix A > 0c > 1 and N > 0. Choose a number x ∈ [0,1] uniformly randomly. How many rational numbers p/q exist such that |x - p/q| < A/q2, where q is an integer in [N, cN]? We will use the dynamics of the horocyclic flow on the space of lattices on 2 to provide an answer to this question as N → ∞.