On the distribution of the sequence (nα) with transcendental α
Christoph Baxa
Acta Arithmetica, Tome 80 (1997), p. 357-363 / Harvested from The Polish Digital Mathematics Library
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     author = {Christoph Baxa},
     title = {On the distribution of the sequence (n$\alpha$) with transcendental $\alpha$},
     journal = {Acta Arithmetica},
     volume = {80},
     year = {1997},
     pages = {357-363},
     zbl = {0886.11046},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav81i4p357bwm}
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Christoph Baxa. On the distribution of the sequence (nα) with transcendental α. Acta Arithmetica, Tome 80 (1997) pp. 357-363. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav81i4p357bwm/

[000] [1] A. Baker, Continued fractions of transcendental numbers, Mathematika 9 (1962), 1-8. | Zbl 0105.03903

[001] [2] A. Baker, On Mahler's classification of transcendental numbers, Acta Math. 111 (1964), 97-120. | Zbl 0147.03403

[002] [3] C. Baxa, On the discrepancy of the sequence (nα), J. Number Theory 55 (1995), 94-107. | Zbl 0835.11028

[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] 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.

[006] [7] E. Maillet, Introduction à la théorie des nombres transcendants et des propriétés arithmétiques des fonctions, Gauthier-Villars, Paris, 1906. | Zbl 37.0237.02

[007] [8] O. Perron, Die Lehre von den Kettenbrüchen, Band 1, Teubner, Stuttgart, 1977. | Zbl 43.0283.04

[008] [9] W. M. Schmidt, On simultaneous approximations of two algebraic numbers by rationals, Acta Math. 119 (1967), 27-50. | Zbl 0173.04801

[009] [10] W. M. Schmidt, Simultaneous approximation to algebraic numbers by rationals, ibid. 125 (1970), 189-201. | Zbl 0205.06702

[010] [11] W. M. Schmidt, Irregularities of distribution VII, Acta Arith. 21 (1972), 45-50. | Zbl 0244.10035

[011] [12] W. M. Schmidt, Diophantine Approximation, Lecture Notes in Math. 785, Springer, Berlin, 1980. | Zbl 0421.10019

[012] [13] J. Schoißengeier, On the discrepancy of (nα) II, J. Number Theory 24 (1986), 54-64. | Zbl 0588.10058

[013] [14] J. Schoißengeier, The discrepancy of (nα)n≥1, Math. Ann. 296 (1993), 529-545. | Zbl 0786.11043

[014] [15] W. Sierpiński, Sur la valeur asymptotique d'une certaine somme, Bull. Internat. Acad. Polon. Sci. Lettres Sér. A Sci. Math. 1910, 9-11. | Zbl 41.0282.01

[015] [16] W. Sierpiński, On the asymptotic value of a certain sum, Rozprawy Akademii Umiej/etno/sci w Krakowie, Wydzia/l mat. przyrod. 50 (1910), 1-10 (in Polish).

[016] [17] H. Weyl, Über die Gibbs'sche Erscheinung und verwandte Konvergenzphänomene, Rend. Circ. Mat. Palermo 30 (1910), 377-407. | Zbl 41.0528.02

[017] [18] H. Weyl, Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), 313-352. | Zbl 46.0278.06