Abstract
Jarník gave a relation between the two most classical uniform exponents of Diophantine approximation in dimension 2. In this paper we consider a twisted case, between the classical and the multiplicative one, and we show that no analogue to Jarník’s relation holds.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Davenport, H., Schmidt, W.M.: Approximation to real numbers by algebraic integers. Acta Arith. 15, 393-416 (1969)
German, O.N.: Transference inequalities for multiplicative Diophantine exponents. Tr. Mat. Inst. Steklova. 275(Klassicheskaya i Sovremennaya Matematika v Pole Deyatelnosti Borisa Nikolaevicha Delone), 227-239 (2011)
Harrap, S.: Twisted inhomogeneous Diophantine approximation and badly approximable sets. Acta Arith. 151(1), 55-82 (2012)
Jarník, V.: Zum khintchineschen “Übertragungssatz”. Trav. Inst. Math. Tbilissi 3, 193-212 (1938)
Laurent, M.: Exponents of diophantine approximmation in dimension two. Can. J. Math. 61, 165-189 (2009)
Minkowski, H.: Geometrie der Zahlen. Bibliotheca Mathematica Teubneriana, Band 40. Johnson Reprint Corp., New York-London (1968)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by J. Schoißengeier.
Rights and permissions
About this article
Cite this article
Marnat, A. There is no analogue to Jarník’s relation for twisted Diophantine approximation. Monatsh Math 181, 675–688 (2016). https://doi.org/10.1007/s00605-015-0859-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00605-015-0859-8