English

Mahler's work on the geometry of numbers

History and Overview 2023-09-19 v1 Number Theory

Abstract

Mahler has written many papers on the geometry of numbers. Arguably, his most influential achievements in this area are his compactness theorem for lattices, his work on star bodies and their critical lattices, and his estimates for the successive minima of reciprocal convex bodies and compound convex bodies. We give a, by far not complete, overview of Mahler's work on these topics and their impact.

Keywords

Cite

@article{arxiv.1806.00356,
  title  = {Mahler's work on the geometry of numbers},
  author = {Jan-Hendrik Evertse},
  journal= {arXiv preprint arXiv:1806.00356},
  year   = {2023}
}

Comments

17 pages. This paper will appear in "Mahler Selecta", a volume dedicated to the work of Kurt Mahler and its impact