The densest sequence in the unit circle
Michael Boshernitzan, Jon Chaika
TL;DR
This paper presents a specific sequence on the unit circle that is proven to be the densest possible, characterized by a particular logarithmic formula.
Contribution
It introduces and proves the densest sequence on the unit circle, providing a new explicit example with a unique logarithmic structure.
Findings
Sequence is proven to be the densest on the unit circle.
Explicit formula for the sequence involving logarithms.
Establishes a new extremal property for sequences on the circle.
Abstract
We exhibit the densest sequence on the unit circle R/Z, x_k= log(2k-1)/log(2) (mod 1).
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Taxonomy
TopicsAnalytic Number Theory Research · Coding theory and cryptography · Mathematical Dynamics and Fractals