2024/09/25 by Shreyasi Datta, Datta, Shreyasi, Nattalie Tamam +1
Computer Science · Mathematics · #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Inequalities and Applications #Matrix Theory and Algorithms #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2409.17105
openalex publication_date 2024/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the notion of weighted singular vectors and weighted uniform exponent with respect to a set of weights. We prove invariance of these exponents for affine subspaces and submanifolds inside those affine subspaces. For certain analytic submanifolds, we show that there are totally irrational vectors with high weighted uniform exponent, extending the previously known existence results. Moreover, we show existence and non-existence of non-obvious divergence orbits for certain cones.