Dirichlet spectrum for one linear form

Schleischitz J.

Bulletin of the London Mathematical Society, vol.55, no.3, pp.1330-1339, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 55 Issue: 3
  • Publication Date: 2023
  • Doi Number: 10.1112/blms.12793
  • Journal Name: Bulletin of the London Mathematical Society
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.1330-1339
  • Middle East Technical University Affiliated: Yes

Abstract

© 2023 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.For (Formula presented.), we determine the Dirichlet spectrum in (Formula presented.) with respect to a linear form and the maximum norm as the entire interval [0, 1]. This natural result improves on the recent work of Beresnevich et al. and complements a subsequent paper by the authors where the analogous result was proved for simultaneous approximation. Various generalizations that can be obtained by similar methods as in the latter paper are indicated. We believe that our results are an important step toward resolving the very open analogous problem for a general system of linear forms.