Abstract
We prove a general metric inequality and give some applications of it to problems in diophantine approximation and to some estimates for general ‘best approximation denominators’, thereby generalising for example results of Khintchine and Schmidt.
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References
CASSELS, J.W.S.: An Introduction to the geometry of numbers. Springer, Berlin (1959).
DAVENPORT, H.: Note on Irregularities of Distribution. Mathematica 3, 131–135 (1956).
KHINTCHINE, A.: Ein Satz über Kettenbrüche mit arithmetischen Anwendungen. Math.Z. 18, 289–306 (1923).
KUIPERS, L. and NIEDERREITER, H.: Uniform distribution of sequences. Wiley, New York (1974).
LAGARIAS, J.: Best Simultaneous Diophantine Approximations I. Trans.Amer.Math.Soc. 272, 545–554 (1982).
SCHMIDT, W.M.: Metrical Theorems on fractional parts of sequences. Trans.Amer.Math.Soc. 110, 493–518 (1964).
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© 1990 Springer-Verlag
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Larcher, G. (1990). An inequality with applications in diophantine approximation. In: Hlawka, E., Tichy, R.F. (eds) Number-Theoretic Analysis. Lecture Notes in Mathematics, vol 1452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096986
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DOI: https://doi.org/10.1007/BFb0096986
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