
TL;DR
This paper introduces divisor divisibility sequences derived from Laurent polynomials evaluated at roots of unity, exploring their divisibility, factorization, and growth, with explicit factorizations and bounds on special sets.
Contribution
It provides the first complete factorization of these sequences for generic polynomials and analyzes the size of rank-of-apparition sets.
Findings
Complete factorization for generic coefficients
Bounds on the size of rank-of-apparition sets
Analytic estimates on growth and divisibility properties
Abstract
We define the associated to a Laurent polynomial to be the sequence , where range over all 'th roots of unity with . More generally, we define analogously for any finite subgroup . We investigate divisibility, factorization, and growth properties of as a function of . In particular, we give the complete factorization of when has generic coefficients, and we prove an analytic estimate showing that the rank-of-apparition sets for are not too large.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
