Approximation to irrationals by classes of rational numbers

Approximation to irrationals by classes of rational numbers
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Proc. Amer. Math. Soc. 6 (1955), 260-264

DOI: https://doi.org/10.1090/S0002-9939-1955-0068590-1

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References

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S. Hartman, Sur une condition supplémentaire dans les approximations diophantiques, Colloq. Math. 2 (1949), 48–51 (French). MR 41174, DOI 10.4064/cm-2-1-48-51
A. Hurwitz, Ueber die angenäherte Darstellung der Irrationalzahlen durch rationale Brüche, Math. Ann. 39 (1891), no. 2, 279–284 (German). MR 1510702, DOI 10.1007/BF01206656

Diophantische Approximationen

J. F. Koksma, Sur l’approximation des nombres irrationnels sous une condition supplémentaire, Simon Stevin 28 (1951), 199–202 (French). MR 47082
L. Kuipers and B. Meulenbeld, Some properties of continued fractions, Acta Math. 87 (1952), 1–12. MR 48505, DOI 10.1007/BF02392279
L. Kuipers and B. Meulenbeld, On a certain classification of the convergents of a continued fraction. I, Nieuw Arch. Wisk. (3) 1 (1953), 199–211. MR 59320
Alexander Oppenheim, Rational approximations to irrationals, Bull. Amer. Math. Soc. 47 (1941), 602–604. MR 5412, DOI 10.1090/S0002-9904-1941-07517-8
Georges Poitou and Roger Descombes, Sur certains problèmes d’approximation. II, C. R. Acad. Sci. Paris 234 (1952), 1522–1524 (French). MR 47722
Raphael M. Robinson, The approximation of irrational numbers by fractions with odd or even terms, Duke Math. J. 7 (1940), 354–359. MR 3009
W. T. Scott, Approximation to real irrationals by certain classes of rational fractions, Bull. Amer. Math. Soc. 46 (1940), 124–129. MR 1246, DOI 10.1090/S0002-9904-1940-07152-6