Abstract

In this paper, we consider singular systems of linear forms over global function fields of class number one and give an upper bound for the Hausdorff dimension of the set of singular systems of linear forms by constructing an appropriate Margulis height function on the space of lattices over global function fields. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.


http://dx.doi.org/10.1016/j.jnt.2026.01.010