Problems and results on diophantine approximations

 Access to full text

 Full (PDF)

1. J.F. Koksma [1] Diophantische Approximationen, Ergebnisse Math. u. Grenzgeb. Vol. 4 Heft 4, Berlin1936. Zbl0012.39602JFM62.0173.01
2. J. Cigler and G. Helmberg [2] Neuere Entwicklungen der Theorie der Gleichverteilung, Jahresbericht D.M.V.64 (1961), 1-50. Zbl0109.03404MR125102
3. P. Erdös [3] Some unsolved problems, Publ. Math. Inst. Hung. Acad. Sci.6 (1961), 221-254. Zbl0100.02001MR177846
4. T. Van Aardenne-Ehrenfest [4] On the impossibility of a just distribution, Indigationes math. 11 (1949), 264-269. Zbl0035.32002MR32717
5. K.F. RothOn irregularities of distribution, Mathematika,1 (1954), 73-79. Zbl0057.28604MR66435
6. 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 JFM53.0073.12
7. R. RadoStudien zur Kombinatorik, Math. Zeitschrift36 (1933) 424 - 480. Zbl0006.14603MR1545354JFM59.0896.13
8. P. Erdös and G. Szekeres [6] On the product Πnk-1(1-zak), Acad. Serbe des Sci.13 (1959), 29 - 34. Zbl0097.03302
9. F.V. Atkinson [7] On a problem of Erdös and Szekeres. Canadian Math. Bull.4 (1961), 7-12. Zbl0119.04304MR126426
10. 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. Zbl0032.26902MR27895
11. J.F. Koksma [9] Some theorems on diophantine inequalities, Math. Centrum Amsterdam Scriptum5 (1950), Zbl0038.02803MR38379
12. P. Szüsz On a problem in the theory of uniform distribution (written in Hungarian) C.r. first Hungarian Math. Congress 461-472 (1952). Zbl0048.28001
13. P. Erdös and P. Turán [10] On the distribution of roots of polynomials, Annals of Math.51 (1950), 105-119. Zbl0036.01501MR33372
14. I.M. Vinogradov [11] Über die Abschätzung trigonometrischer Summen mit Primzahlen, Isvestija Akad. Nauk. SSSR Ser. mat12 (1948), 225 - 248. Zbl0033.16401
15. J.W.S. Cassels [12] Some metrical theorems in diophantine approximation, Proc. Cambridge Phil. Soc.46 (1950), 209-218. Zbl0035.31902MR36787
16. P. Erdös and J.F. Koksma [13] On the uniform distribution mod 1 of sequences {f(n, θ)}, Indig. Math.11 (1949), 299-302. Zbl0035.32101
17. P. Erdös and I.S. Gál [13] On the law of the iterated logarithm, Indig. Math.17 (1955) 65-84. Zbl0068.05403MR69309
18. A.J. Khintchine [14] Ein Satz über Kettenbruche mit arithmetischen Anwendungen, Math. Zeitschrift18 (1923), 289-306, see p. 303 - 304. Zbl49.0159.03MR1544632JFM49.0159.03
19. F. Riesz [15] Sur la théorie ergodique, Comment. Math. Helv.17 (1945), 221- 289. Zbl0063.06500MR14218
20. P. Erdös [16] On the strong law of large numbers, Trans. Amer. Math. Soc.67 (1949), 51-56. Zbl0034.07201MR32971
21. J.F. Koksma [17] Estimations de fonctions à l'aide d'intégrales de Lebesgue, Bull. Soc. Math. Belg.6 (1958-54) 4-18. Zbl0058.04902MR67177
22. E. Hlawka [18] Zur formalen Theorie der Gleichverteilung in kompakten Gruppen, Rend. Cise. Mat. Palermo4 (1955), 33-47. Zbl0065.26402MR74489
23. G.M. PetersenAlmost convergence and uniformly distributed sequences, quarterly J. of Math.OxfordII Ser. 7 (1956), 188-191. Zbl0072.28302MR95812
24. See also F.R. Keogh, B. Lawton and G.M. Petersen, Well distributed sequences, Canad. J. Math.10 (1958), 572-576. Zbl0085.27103MR95813
25. A.J. Khintchine [19] Einige Sätze über Kettenbrüche mit Anwendungen auf die Theorie der Diophantischen ApproximationenMath. Ann.92 (1924), 115 —125. Zbl50.0125.01JFM50.0125.01
26. R.J. Duffin and A.C. Schaeffer [20] Khintchine's problem in metric diophantine approximation, Duke Math. J.8 (1941), 243 - 255, Zbl0025.11002MR4859JFM67.0145.03
27. J.W.S. Cassels, Some metrical theorems in diophantine approximation I. Proc. Cambridge Phil. Soc.46 (1950), 209 - 218. Zbl0035.31902MR36787
28. S. Hartman and P. Szüsz [21] On congruence classes of denominators of convergents, Acta Arith.6 (1960), 179-184. See also Zbl0094.25804MR117189
29. P. SzüszVerallgemeinerung und Anwendungen eines Kusminschen Satzes, ibid.7 (1962),149-160, Zbl0104.27401MR153621
30. and P. Süsz, Über die metrische Theorie der Diophantischen Approximationen (will soon appear in Acta Arith.). 
31. E. Hecke [22] Über analytische Funktionen und die Verteilung der Zahlen mod 1, Abh. math. Semin. Hamburg Univ.1 (1922) 54-76, Zbl48.0197.03JFM48.0197.03
32. A. OstrowskiMiszellen 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). JFM56.0184.01
33. P. Erdös, P. Szusz and P. Turán [23] Remarks on the theory of diophantine approximation, Coll. Math.6 (1958), 119-126. Zbl0087.04305MR102498
34. H. Kesten [24] Some probabilistic theorems on diophantine approximations, Trans. Amer. Math. Soc.103 (1962), 189-217. Zbl0105.03805MR137692
35. H. Kesten [25] Uniform distribution mod 1, Annals of Math.71 (1960), 445-471. Zbl0101.03803MR113864
36. W.J. Leveque [26] On uniform distribution modulo a subdivision, Pacific J. of Math.3 (1953), 757-771. Zbl0051.28503MR59323

1. R. Tijdeman, M. Voorhoeve, Bounded discrepancy sets
2. Wolfgang M. Schmidt, Irregularities of distribution. VI
3. Jacques Lesca, Sur la répartition modulo 1 des suites $\left(n\alpha \right)$
4. Pierre Liardet, Regularities of distribution