The irrationality measure of π as seen through the eyes of cos(n)

2018/07/09 by Chen, Sully F., Pearse, Erin P. J.
#11J82 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1807.02955

Abstract

For different values of γ≥ 0, analysis of the end behavior of the sequence a_n = cos (n)^nγ yields a strong connection to the irrationality measure of π. We show that if \limsup |cos n|ⁿ² ≠ 1, then the irrationality measure of π is exactly 2. We also give some numerical evidence to support the conjecture that μ(π)=2, based on the appearance of some startling subsequences of cos(n)ⁿ.

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