Abstract
The first question is about a possible variation on Dirichlet's approximation theorem for linear forms αx+βy+z, wherex,y are restricted topositive integers. The second question, which turns out to be related to the first, is about approximation to elements in a power series fieldk((t −1)) by solutions β of first order linear differential equationsxβ′+yβ+z=0, wherex,y,z are polynomials int.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Davenport, H., andW. Schmidt: Approximation to real numbers by quadratic irrationals. Acta Arith.13, 169–176 (1967).
Davenport, H., andW. Schmidt: A theorem on linear forms. Acta Arith.14, 209–223 (1968).
Obréskov, N.: On Diophantine approximations of linear forms for positive values of the variables. Dokl. Akad. Nauk. SSSR73, 21–24 (1950).
Rogers, C. A.: The signatures of the errors of simultaneous Diophantine approximations. Proc. Lond. Math. Soc. (2)52, 186–190 (1951).
Author information
Authors and Affiliations
Additional information
Dedicated to Prof. Dr. E. Hlawka on the occasion of his 60th birthday
Rights and permissions
About this article
Cite this article
Schmidt, W.M. Two questions in diophantine approximation. Monatshefte für Mathematik 82, 237–245 (1976). https://doi.org/10.1007/BF01526328
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF01526328