• [1] J. W. S. Cassels, Über , Math. Ann. vol. 127 (1954) pp. 288-304. MR 0060546 (15:687d)
• [2] -, An introduction to Diophantine approximations, Cambridge Tracts No. 45, Cambridge, 1957.
• [3] J. H. H. Chalk, Rational approximations in the complex plane. II, J. London Math. Soc. vol. 31 (1956) pp. 216-221. MR 0077578 (17:1061a)
• [4] R. Descombes, Sur la répartition des sommets d'une ligne polygonale régulière non fermée, Ann. Sci. École Norm. Sup. vol. 73 (1956) pp. 283-355. MR 0086844 (19:253b)
• [5] G. H. Hardy and E. M. Wright, The theory of numbers, 3rd ed., Oxford, Clarendon Press, 1954. MR 0067125 (16:673c)
• [6] S. Hartman, Sur une condition supplémentaire dans les approximations diophantiques, Colloq. Math. vol. 2 (1949) pp. 48-51. MR 0041174 (12:807a)
• [7] E. Hlawka, Über die Approximation von zwei komplexen inhomogenen Linearformen, Monatsh. Math. vol. 46 (1937-1938) pp. 324-334. MR 1550750
• [8] A. Hurwitz, Über die angenäherte Darstellung der Irrationalzahlen durch rationale Brüche, Math. Ann. vol. 39 (1891) pp. 279-284. MR 1510702
• [9] A. Khintchine, Neuer Beweis und Verallgemeinerung eines Hurwitzschen Satzes, Math. Ann. vol. 111 (1935) pp. 631-637. MR 1513020
• [10] J. F. Koksma, Sur l'approximation des nombres irrationels sous une condition supplémentaire, Simon Stevin vol. 28 (1951) pp. 199-202. MR 0047082 (13:825e)
• [11] L. Kuipers and B. Meulenbeld, Some properties of continued fractions, Acta Math. vol. 87 (1952) pp. 1-12. MR 0048505 (14:23d)
• [12] W. J. LeVeque, On asymmetric approximations, Michigan Math. J. vol. 2 (1953) pp. 1-6. MR 0062784 (16:18b)
• [13] K. Mahler, On the product of two complex linear polynomials in two variables, J. London Math. Soc. vol. 15 (1940) pp. 213-236. MR 0003006 (2:148e)
• [14] M. Müller, Über die Approximation reeler Zahlen durch die Näherungsbrüche ihres regelmässigen Kettenbruches, Arch. Math. vol. 6 (1955) pp. 253-258. MR 0069850 (16:1090e)
• [15] Ivan Niven, Irrational numbers, Carus Monograph No. 11, New York, John Wiley, 1956. MR 0080123 (18:195c)
• [16] Nicolae Negoescu, Quelques précisions concernant le théorème de M. B. Segre sur des approximations asymetriques des nombres irrationnels par les rationnels, Bull. École Polytech. Jassy, vol. 3 (1948) pp. 3-16. MR 0027011 (10:235d)
• [17] -, Note on a theorem of unsymmetric approximation, Acad. R. P. Romine Bul. Şti. Secţ. Şti. Mat. Fiz. vol. 1 (1949) pp. 115-117. MR 0045772 (13:630d)
• [18] N. Obrechkoff, Sur l'approximation des nombres irrationnels par des nombres rationnels, C. R. Acad. Bulgare Sci. vol. 3 (1950) pp. 1-4 (Russian). MR 0043848 (13:329a)
• [19] C. D. Olds, Note on an asymmetric Diophantine approximation, Bull. Amer. Math. Soc. vol. 52 (1946) pp. 261-263. MR 0017758 (8:196e)
• [20] Alexander Oppenheim, Rational approximations to irrationals, Bull. Amer. Math. Soc. vol. 47 (1941) pp. 602-604. MR 0005412 (3:150b)
• [21] A. V. Prasad, Note on a theorem of Hurwitz, J. London Math. Soc. vol. 23 (1948) pp. 169-171. MR 0028883 (10:513d)
• [22] R. M. Robinson, The approximation of irrational numbers by fractions with odd or even terms, Duke Math. J. vol. 7 (1940) pp. 354-359. MR 0003009 (2:149c)
• [23] -, Unsymmetrical approximation of irrational numbers, Bull. Amer. Math. Soc. vol. 53 (1947) pp. 351-361. MR 0020583 (8:566b)
• [24] W. T. Scott, Approximation to real irrationals by certain classes of rational fractions, Bull. Amer. Math. Soc. vol. 46 (1940) pp. 124-129. MR 0001246 (1:203a)
• [25] B. Segre, Lattice points in infinite domains and asymmetric Diophantine approximations, Duke Math. J. vol. 12 (1945) pp. 337-365. MR 0012096 (6:258a)
• [26] V. T. Sós, On the theory of Diophantine approximations. II. Inhomogeneous problems, Acta Math. Acad. Sci. Hungar. vol. 9 (1958) pp. 229-241. MR 0095164 (20:1670)
• [27] Leonard Tornheim, Asymmetric minima of quadratic forms and asymmetric Diophantine approximation, Duke Math. J. vol. 22 (1955) pp. 287-294. MR 0069221 (16:1003a)

Bibliography

[1]

J. W. S. Cassels, Über , Math. Ann. vol. 127 (1954) pp. 288-304. MR 0060546 (15:687d)

[2]

-, An introduction to Diophantine approximations, Cambridge Tracts No. 45, Cambridge, 1957.

[3]

J. H. H. Chalk, Rational approximations in the complex plane. II, J. London Math. Soc. vol. 31 (1956) pp. 216-221. MR 0077578 (17:1061a)

[4]

R. Descombes, Sur la répartition des sommets d'une ligne polygonale régulière non fermée, Ann. Sci. École Norm. Sup. vol. 73 (1956) pp. 283-355. MR 0086844 (19:253b)

[5]

G. H. Hardy and E. M. Wright, The theory of numbers, 3rd ed., Oxford, Clarendon Press, 1954. MR 0067125 (16:673c)

[6]

S. Hartman, Sur une condition supplémentaire dans les approximations diophantiques, Colloq. Math. vol. 2 (1949) pp. 48-51. MR 0041174 (12:807a)

[7]

E. Hlawka, Über die Approximation von zwei komplexen inhomogenen Linearformen, Monatsh. Math. vol. 46 (1937-1938) pp. 324-334. MR 1550750

[8]

A. Hurwitz, Über die angenäherte Darstellung der Irrationalzahlen durch rationale Brüche, Math. Ann. vol. 39 (1891) pp. 279-284. MR 1510702

[9]

A. Khintchine, Neuer Beweis und Verallgemeinerung eines Hurwitzschen Satzes, Math. Ann. vol. 111 (1935) pp. 631-637. MR 1513020

[10]

J. F. Koksma, Sur l'approximation des nombres irrationels sous une condition supplémentaire, Simon Stevin vol. 28 (1951) pp. 199-202. MR 0047082 (13:825e)

[11]

L. Kuipers and B. Meulenbeld, Some properties of continued fractions, Acta Math. vol. 87 (1952) pp. 1-12. MR 0048505 (14:23d)

[12]

W. J. LeVeque, On asymmetric approximations, Michigan Math. J. vol. 2 (1953) pp. 1-6. MR 0062784 (16:18b)

[13]

K. Mahler, On the product of two complex linear polynomials in two variables, J. London Math. Soc. vol. 15 (1940) pp. 213-236. MR 0003006 (2:148e)

[14]

M. Müller, Über die Approximation reeler Zahlen durch die Näherungsbrüche ihres regelmässigen Kettenbruches, Arch. Math. vol. 6 (1955) pp. 253-258. MR 0069850 (16:1090e)

[15]

Ivan Niven, Irrational numbers, Carus Monograph No. 11, New York, John Wiley, 1956. MR 0080123 (18:195c)

[16]

Nicolae Negoescu, Quelques précisions concernant le théorème de M. B. Segre sur des approximations asymetriques des nombres irrationnels par les rationnels, Bull. École Polytech. Jassy, vol. 3 (1948) pp. 3-16. MR 0027011 (10:235d)

[17]

-, Note on a theorem of unsymmetric approximation, Acad. R. P. Romine Bul. Şti. Secţ. Şti. Mat. Fiz. vol. 1 (1949) pp. 115-117. MR 0045772 (13:630d)

[18]

N. Obrechkoff, Sur l'approximation des nombres irrationnels par des nombres rationnels, C. R. Acad. Bulgare Sci. vol. 3 (1950) pp. 1-4 (Russian). MR 0043848 (13:329a)

[19]

C. D. Olds, Note on an asymmetric Diophantine approximation, Bull. Amer. Math. Soc. vol. 52 (1946) pp. 261-263. MR 0017758 (8:196e)

[20]

Alexander Oppenheim, Rational approximations to irrationals, Bull. Amer. Math. Soc. vol. 47 (1941) pp. 602-604. MR 0005412 (3:150b)

[21]

A. V. Prasad, Note on a theorem of Hurwitz, J. London Math. Soc. vol. 23 (1948) pp. 169-171. MR 0028883 (10:513d)

[22]

R. M. Robinson, The approximation of irrational numbers by fractions with odd or even terms, Duke Math. J. vol. 7 (1940) pp. 354-359. MR 0003009 (2:149c)

[23]

-, Unsymmetrical approximation of irrational numbers, Bull. Amer. Math. Soc. vol. 53 (1947) pp. 351-361. MR 0020583 (8:566b)

[24]

W. T. Scott, Approximation to real irrationals by certain classes of rational fractions, Bull. Amer. Math. Soc. vol. 46 (1940) pp. 124-129. MR 0001246 (1:203a)

[25]

B. Segre, Lattice points in infinite domains and asymmetric Diophantine approximations, Duke Math. J. vol. 12 (1945) pp. 337-365. MR 0012096 (6:258a)

[26]

V. T. Sós, On the theory of Diophantine approximations. II. Inhomogeneous problems, Acta Math. Acad. Sci. Hungar. vol. 9 (1958) pp. 229-241. MR 0095164 (20:1670)

[27]

Leonard Tornheim, Asymmetric minima of quadratic forms and asymmetric Diophantine approximation, Duke Math. J. vol. 22 (1955) pp. 287-294. MR 0069221 (16:1003a)