@article{bwmeta1.element.bwnjournal-article-aav68i3p281bwm, author = {C. Baxa and J. Schoissengeier}, title = {Minimum and maximum order of magnitude of the discrepancy of (n$\alpha$)}, journal = {Acta Arithmetica}, volume = {68}, year = {1994}, pages = {281-290}, zbl = {0828.11038}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav68i3p281bwm} }
C. Baxa; J. Schoissengeier. Minimum and maximum order of magnitude of the discrepancy of (nα). Acta Arithmetica, Tome 68 (1994) pp. 281-290. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav68i3p281bwm/
[000] [1] C. Baxa, Die maximale Größ enordnung der Diskrepanz der Folge , Dissertation, Universität Wien, 1993.
[001] [2] C. Baxa, On the discrepancy of the sequence (nα), to appear.
[002] [3] H. Behnke, Über die Verteilung von Irrationalitäten mod 1, Abh. Math. Sem. Univ. Hamburg 1 (1922), 252-267. | Zbl 48.0186.01
[003] [4] H. Behnke, Zur Theorie der diophantischen Approximationen I, Abh. Math. Sem. Univ. Hamburg 3 (1924), 261-318. | Zbl 50.0124.03
[004] [5] P. Bohl, Über ein in der Theorie der säkularen Störungen vorkommendes Problem, J. Reine Angew. Math. 135 (1909), 189-283. | Zbl 40.1005.03
[005] [6] T. W. Cusick and M. E. Flahive, The Markoff and Lagrange Spectra, Math. Surveys Monographs 30, Amer. Math. Soc., Providence, Rhode Island, 1989. | Zbl 0685.10023
[006] [7] Y. Dupain, Répartition et discrépance, Thèse, Université de Bordeaux I, 1978.
[007] [8] Y. Dupain, Discrépance de la suite ({n((1+√5)/2)}), Ann. Inst. Fourier (Grenoble) 29 (1979), 81-106.
[008] [9] Y. Dupain and V. T. Sós, On the discrepancy of (nα) sequences, in: Topics in Classical Number Theory, Vol. 1, Colloq. Math. Soc. János Bolyai 34, G. Halász (ed.), North-Holland, Amsterdam, 1984, 355-387.
[009] [10] G. H. Hardy and J. E. Littlewood, Some problems of Diophantine Approximation: The lattice points of a right-angled triangle II, Abh. Math. Sem. Univ. Hamburg 1 (1922), 212-249.
[010] [11] E. Hecke, Über analytische Funktionen und die Verteilung von Zahlen mod. Eins, Abh. Math. Sem. Univ. Hamburg 1 (1922) 54-76. | Zbl 48.0197.03
[011] [12] J. Lesca, Sur la répartition modulo 1 de la suite nα, Acta Arith. 20 (1972), 345-352. | Zbl 0239.10018
[012] [13] H. Niederreiter, Application of diophantine approximation to numerical integration, in: Diophantine Approximation and Its Applications, C. F. Osgood (ed.), Academic Press, New York, 1973, 129-199.
[013] [14] A. Ostrowski, Bemerkungen zur Theorie der Diophantischen Approximationen, Abh. Math. Sem. Univ. Hamburg 1 (1922), 77-98. | Zbl 48.0185.01
[014] [15] L. Ramshaw, On the discrepancy of the sequence formed by the multiples of an irrational number, J. Number Theory 13 (1981), 138-175. | Zbl 0458.10035
[015] [16] W. M. Schmidt, Irregularities of distribution VII, Acta Arith. 21 (1972), 45-50. | Zbl 0244.10035
[016] [17] J. Schoißengeier, On the discrepancy of (nα), Acta Arith. 44 (1984), 241-279. | Zbl 0506.10031
[017] [18] J. Schoißengeier, On the discrepancy of (nα) II, J. Number Theory 24 (1986), 54-64. | Zbl 0588.10058
[018] [19] J. Schoißengeier, Abschätzungen für , Monatsh. Math. 102 (1986), 59-77.
[019] [20] J. Schoißengeier, The discrepancy of , Math. Ann. 296 (1993), 529-545. | Zbl 0786.11043
[020] [21] W. Sierpi/nski, Sur la valeur asymptotique d'une certaine somme, Bull. Int. Acad. Polon. Sci. (Cracovie) A (1910), 9-11. | Zbl 41.0282.01
[021] [22] W. Sierpi/nski, On the asymptotic value of a certain sum, Rozprawy Akademii Umiej/etno/sci w Krakowie, Wydział mat. przyrod. 50 (1910), 1-10 (in Polish).
[022] [23] V. T. Sós, On the theory of diophantine approximation II (inhomogeneous problems), Acta Math. Acad. Sci. Hungar. 9 (1958), 229-241. | Zbl 0086.03902
[023] [24] V. T. Sós, On strong irregularities of the distribution of {nα} sequences, in: Studies in Pure Mathematics, P. Erdős (ed.), Birkhäuser, Boston, 1983, 685-700.
[024] [25] H. Weyl, Über die Gibbs'sche Erscheinung und verwandte Konvergenzphänomene, Rend. Circ. Mat. Palermo 30 (1910), 377-407. | Zbl 41.0528.02
[025] [26] H. Weyl, Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), 313-352 | Zbl 46.0278.06