×

zbMATH — the first resource for mathematics

On a series of cosecants related to a problem in ergodic theory. (English) Zbl 0269.10030

MSC:
11K60 Diophantine approximation in probabilistic number theory
40A99 Convergence and divergence of infinite limiting processes
28D05 Measure-preserving transformations
11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.
PDF BibTeX XML Cite
Full Text: Numdam EuDML
References:
[1] P. Bohl [1] Über ein in der Theorie der säkulären Störungen vorkommendes Problem , Jour. f. d. reine und angew. Math. 135 (1909) 189-283. · JFM 40.1005.03
[2] P.L. Butzer and U. Westphal [2] The mean ergodic theorem and saturation , Indiana Univ. Math. Jour. 20 (1970/71) 1163-1174. · Zbl 0206.43402 · doi:10.1512/iumj.1971.20.20107
[3] H. Furstenberg , H. Keynes and L. Shapiro [3] Prime flows in topological dynamics , in preparation. · Zbl 0264.54030 · doi:10.1007/BF02761532
[4] W.H. Gottschalk and G.A. Hedlund [4] Topological Dynamics , A.M.S. Coll. Pubs. Vol. XXXVI, Providence, R. I., 1955. · Zbl 0067.15204
[5] E. Hecke [5] Analytische Funktionen und die Verteilung von Zahlen mod. eins , Abh. Math. Semin. Hamburg Univ. 1 (1922) 54-76. · JFM 48.0197.03
[6] M. Kac and R. Salem [6] On a series of cosecants , K. Akad. v. Wet. Amsterdam Proc. (Series A) 60 (1957) 265-267. · Zbl 0080.04301
[7] H. Kesten [7] On a conjecture of Erdös and Szüsz related to uniform distribution mod 1 , Acta Arith. 12 (1966) 193-212. · Zbl 0144.28902 · eudml:204796
[8] A. Ostrowski [8] Notiz zur Theorie der Diophantischen Approximationen und zur Theorie der linearen Diophantischen Approximationen , Jahresber. d. Deutschen Math. Ver. 36 (1927) 178-180 and 39 (1930) 34-46. · JFM 56.0184.01
[9] K. Petersen [9] Spectra of induced transformations, Recent Advances in Topological Dynamics , Springer-Verlag, New York, 1973, 226-230. · Zbl 0255.28013
[10] L. Shapiro [10] Irregularities of distribution in dynamical systems, Recent Advances in Topological Dynamics , Springer-Verlag, New York, 1973, 249-252 · Zbl 0255.54034
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.