Problems and results on diophantine approximations
Compositio Mathematica, Tome 16 (1964), pp. 52-65.
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     author = {Erd\"os, P.},
     title = {Problems and results on diophantine approximations},
     journal = {Compositio Mathematica},
     pages = {52--65},
     publisher = {Kraus Reprint},
     volume = {16},
     year = {1964},
     mrnumber = {179131},
     zbl = {0131.04803},
     language = {en},
     url = {http://archive.numdam.org/item/CM_1964__16__52_0/}
}
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Erdös, P. Problems and results on diophantine approximations. Compositio Mathematica, Tome 16 (1964), pp. 52-65. http://archive.numdam.org/item/CM_1964__16__52_0/

J.F. Koksma [1] Diophantische Approximationen, Ergebnisse Math. u. Grenzgeb. Vol. 4 Heft 4, Berlin 1936. | JFM | Zbl

J. Cigler and G. Helmberg [2] Neuere Entwicklungen der Theorie der Gleichverteilung, Jahresbericht D.M.V. 64 (1961), 1-50. | MR | Zbl

P. Erdös [3] Some unsolved problems, Publ. Math. Inst. Hung. Acad. Sci. 6 (1961), 221-254. | MR | Zbl

T. Van Aardenne-Ehrenfest [4] On the impossibility of a just distribution, Indigationes math. 11 (1949), 264-269. | MR | Zbl

K.F. Roth On irregularities of distribution, Mathematika,1 (1954), 73-79. | MR | Zbl

B.L. Van Der Waerden [5] Beweis einer Baudetschen Vermutung, Archiv Viskunde (2) 15 (1928), 212 - 216, for further problems and results in this direction see | JFM

R. Rado Studien zur Kombinatorik, Math. Zeitschrift 36 (1933) 424 - 480. | JFM | MR | Zbl

P. Erdös and G. Szekeres [6] On the product Πnk-1(1-zak), Acad. Serbe des Sci. 13 (1959), 29 - 34. | Zbl

F.V. Atkinson [7] On a problem of Erdös and Szekeres. Canadian Math. Bull. 4 (1961), 7-12. | MR | Zbl

P. Erdös and P. Turán [8] On a problem in the theory of uniform distribution I, II. Indigationes math. 10 (1948) 370-378, 406-413. | MR | Zbl

J.F. Koksma [9] Some theorems on diophantine inequalities, Math. Centrum Amsterdam Scriptum 5 (1950), | MR | Zbl

P. Szüsz On a problem in the theory of uniform distribution (written in Hungarian) C.r. first Hungarian Math. Congress 461-472 (1952). | Zbl

P. Erdös and P. Turán [10] On the distribution of roots of polynomials, Annals of Math. 51 (1950), 105-119. | MR | Zbl

I.M. Vinogradov [11] Über die Abschätzung trigonometrischer Summen mit Primzahlen, Isvestija Akad. Nauk. SSSR Ser. mat 12 (1948), 225 - 248. | Zbl

J.W.S. Cassels [12] Some metrical theorems in diophantine approximation, Proc. Cambridge Phil. Soc. 46 (1950), 209-218. | MR | Zbl

P. Erdös and J.F. Koksma [13] On the uniform distribution mod 1 of sequences {f(n, θ)}, Indig. Math. 11 (1949), 299-302. | Zbl

P. Erdös and I.S. Gál [13] On the law of the iterated logarithm, Indig. Math. 17 (1955) 65-84. | MR | Zbl

A.J. Khintchine [14] Ein Satz über Kettenbruche mit arithmetischen Anwendungen, Math. Zeitschrift 18 (1923), 289-306, see p. 303 - 304. | JFM | MR

F. Riesz [15] Sur la théorie ergodique, Comment. Math. Helv. 17 (1945), 221- 289. | MR | Zbl

P. Erdös [16] On the strong law of large numbers, Trans. Amer. Math. Soc. 67 (1949), 51-56. | MR | Zbl

J.F. Koksma [17] Estimations de fonctions à l'aide d'intégrales de Lebesgue, Bull. Soc. Math. Belg. 6 (1958-54) 4-18. | MR | Zbl

E. Hlawka [18] Zur formalen Theorie der Gleichverteilung in kompakten Gruppen, Rend. Cise. Mat. Palermo 4 (1955), 33-47. | MR | Zbl

G.M. Petersen Almost convergence and uniformly distributed sequences, quarterly J. of Math. Oxford II Ser. 7 (1956), 188-191. | MR | Zbl

See also F.R. Keogh, B. Lawton and G.M. Petersen, Well distributed sequences, Canad. J. Math. 10 (1958), 572-576. | MR | Zbl

A.J. Khintchine [19] Einige Sätze über Kettenbrüche mit Anwendungen auf die Theorie der Diophantischen Approximationen Math. Ann. 92 (1924), 115 -125. | JFM

R.J. Duffin and A.C. Schaeffer [20] Khintchine's problem in metric diophantine approximation, Duke Math. J. 8 (1941), 243 - 255, | JFM | MR | Zbl

J.W.S. Cassels, Some metrical theorems in diophantine approximation I. Proc. Cambridge Phil. Soc. 46 (1950), 209 - 218. | MR | Zbl

S. Hartman and P. Szüsz [21] On congruence classes of denominators of convergents, Acta Arith. 6 (1960), 179-184. See also | MR | Zbl

P. Szüsz Verallgemeinerung und Anwendungen eines Kusminschen Satzes, ibid. 7 (1962),149-160, | MR | Zbl

and P. Süsz, Über die metrische Theorie der Diophantischen Approximationen (will soon appear in Acta Arith.).

E. Hecke [22] Über analytische Funktionen und die Verteilung der Zahlen mod 1, Abh. math. Semin. Hamburg Univ. 1 (1922) 54-76, | JFM

A. Ostrowski Miszellen IX and XVI, Notiz zur Theorie der Diophantischen Approximationen und zur Theorie der linearen Diophantischen Approximationen. Jahresbericht der Deutschen Math. Ver. 36 (1927), 178 - 180und 39 (1930), 34-46). | JFM

P. Erdös, P. Szusz and P. Turán [23] Remarks on the theory of diophantine approximation, Coll. Math. 6 (1958), 119-126. | MR | Zbl

H. Kesten [24] Some probabilistic theorems on diophantine approximations, Trans. Amer. Math. Soc. 103 (1962), 189-217. | MR | Zbl

H. Kesten [25] Uniform distribution mod 1, Annals of Math. 71 (1960), 445-471. | MR | Zbl

W.J. Leveque [26] On uniform distribution modulo a subdivision, Pacific J. of Math. 3 (1953), 757-771. | MR | Zbl