Kamae, T.; Mendès France, Michel Van der Corput’s difference theorem. (German) Zbl 0396.10040 Isr. J. Math. 31, 335-342 (1978). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 10 ReviewsCited in 44 Documents MSC: 11K06 General theory of distribution modulo \(1\) 11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension Keywords:Van Der Corput’s Difference Theorem; Uniform Distribution; Sequences Of Integers PDF BibTeX XML Cite \textit{T. Kamae} and \textit{M. Mendès France}, Isr. J. Math. 31, 335--342 (1978; Zbl 0396.10040) Full Text: DOI References: [1] Bass, J., Suites uniformément denses, moyennes, trigonométriques, fonctions pseudo-aléatoires, Bull. Soc. Math. France, 87, 1-64 (1959) · Zbl 0092.33404 [2] Bertrandias, J.-P., Suites pseudo-aléatoires et critères d’équirépartition modulo un, Compositio Math., 16, 23-28 (1964) · Zbl 0207.05801 [3] Cigler, J., The fundamental theorem of van der Corput on uniform distribution and its generalizations, Compositio Math., 16, 29-34 (1964) · Zbl 0147.37102 [4] Coquet, J.; Kamae, T.; Mendes France, M., La mesure spectrale de certaines suites arithmétiques, Bull. Soc. Math. France, 105, 369-384 (1977) · Zbl 0383.10035 [5] Daboussi, H.; France, M., Spectrum, almost periodicity and equidistribution modulo, Studia Sci. Math. Hungar., 9, 173-180 (1974) · Zbl 0321.10043 [6] Elliott, P. D. T. A., On distribution functions (mod 1);quantitative Fourier inversion, J. Number Theory, 4, 509-522 (1972) · Zbl 0253.10042 [7] W. Ellison,Les nombres premiers, Hermann, 1975. · Zbl 0313.10001 [8] Furstenberg, H., Ergodic behavior of diagonal measures and a theorem of Szeméredi on arithmetical progressions, J. Analyse Math., 31, 204-256 (1977) · Zbl 0347.28016 [9] L. Kuipers and H. Niederreiter,Uniform Distribution of Sequences, Wiley (Interscience), 1974. · Zbl 0281.10001 [10] Mendes France, M., Les suites à spectre vide et la répartition (mod 1), J. Number Theory, 5, 1-15 (1973) · Zbl 0252.10033 [11] Niederreiter, H.; Philipp, W., Berry-Esseen bounds and a theorem of Erdos and Turan on uniform distribution mod 1, Duke Math. J., 40, 633-649 (1973) · Zbl 0273.10043 [12] G. Rauzy,Etude de quelques ensembles de fonctions définies par des propriétés de moyenne, Séminaire Théorie des Nombres de Bordeaux 1972-73, exposé 20, 18p. · Zbl 0293.10018 [13] G. Rauzy,Equirépartition et entropie, inRepartition Modulo 1, Lecture Notes in Math., Springer-Verlag475, 1975, pp. 155-175. [14] G. Rauzy,Propriétés statistiques des suites arithmétiques, Collection SUP, PUF, 1976. · Zbl 0337.10036 [15] H. Rindler,Fast Konstante Folgen, preprint. · Zbl 0398.22007 [16] Sárközy, A., On difference sets of sequences of integers I, Acta Math. Acad. Sci. Hungar., 31, 125-149 (1978) · Zbl 0387.10033 [17] A. Sárközy,On difference sets of sequences of integers II, Ann. Univ. Sci. Budapst Eötvös, to appear. · Zbl 0413.10051 [18] A. Sárközy,On difference sets of sequences of integers III, to appear. · Zbl 0387.10034 [19] C. Stewart and R. Tijdeman,On the infinite difference sets of sequences of positive integers, Canad. J. Math., to appear. · Zbl 0524.10044 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.