On Diophantine exponents and Khintchine's transference principle

Abstract

In this paper we improve estimates of Jarnik and Apfelbeck for uniform Diophantine exponents of transposed systems of linear forms and generalize to the case of an arbitrary system the estimates of Laurent and Bugeaud for individual exponents. The method proposed also gives a better constant in Mahler's transference theorem.

19 pages, 19 references

References in corpus (1)

• On transfer inequalities in Diophantine approximation, II

Cited by in corpus (10)

• A variational principle in the parametric geometry of numbers
• On the spectrum of Diophantine approximation constants
• Approximation to an extremal number, its square and its cube
• Diophantine transference inequalities: weighted, inhomogeneous, and intermediate exponents
• Transference inequalities for multiplicative Diophantine exponents
• Geometry of Diophantine exponents
• Going-up theorems for simultaneous Diophantine approximation
• Khintchine's theorem on Chebyshev matrices
• On Wirsing's problem in small exact degree
• Splitting transference inequalities with the help of Wolfgang Schmidt's parametric geometry of numbers