Some applications of the individual ergodic theorem to problems in number theory
Cigler, Johann
Compositio Mathematica, Tome 16 (1964), p. 35-43 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1964-01-01
@article{CM_1964__16__35_0,
     author = {Cigler, Johann},
     title = {Some applications of the individual ergodic theorem to problems in number theory},
     journal = {Compositio Mathematica},
     volume = {16},
     year = {1964},
     pages = {35-43},
     mrnumber = {171894},
     zbl = {0142.29701},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1964__16__35_0}
}

Cigler, Johann. Some applications of the individual ergodic theorem to problems in number theory. Compositio Mathematica, Tome 16 (1964) pp. 35-43. http://gdmltest.u-ga.fr/item/CM_1964__16__35_0/

J.R. Blum and D.L. Hanson [1] On invariant probability measures I, Pacific J. Math. 10, 1125 -1129 (1960). | Zbl 0104.11006

J. Cigler [2] Der individuelle Ergodensatz in der Theorie der Gleichverteilung mod 1, J. reine angew. Math. 205, 91-100 (1960). | MR 176973 | Zbl 0131.29301

J. Cigler [3] Ein gruppentheoretisches Analogon zum Begriff der normalen Zahl, J. reine angew. Math. 206, 5 - 8 (1961). | MR 163924 | Zbl 0103.01902

J. Cigler [4] Ziffernverteilung in v-adischen Brüchen, Math. Zeitschr. 75, 8-13 (1961). | MR 121353 | Zbl 0215.35703

J. Cigler und G. Helmberg [5] Neuere Entwicklungen der Theorie der Gleichverteilung, Jahresber. DMV 64, 1-50 (1961). | MR 125102 | Zbl 0109.03404

A.O. Gelfond [6] Über eine allgemeine Eigenschaft von Zahlsystemen, (russ.), Izvest. Akad. Nauk SSSR, Ser. mat. 23, 809 - 814 (1959). | Zbl 0092.27702

E. Hlawka [7] Folgen auf kompakten Räumen II, Math. Nachr. 18, 188-202 (1958). | MR 99556 | Zbl 0082.04102

J.F. Koksma [8] Ein mengentheoretischer Satz über die Gleichverteilung mod. Eins, Compositio math. 2, 250 - 258 (1935). | JFM 61.0205.01 | Numdam | Zbl 0012.01401

J.E. Maxfield [9] Normal k-tuples, Pacific J. Math. 3, 189 -196 (1953). | MR 53978 | Zbl 0050.27503

I. Niven [10] Irrational Numbers, New York 1956. | MR 80123 | Zbl 0070.27101

W. Parry [11] On the β-expansion of real numbers, Acta math. (hung. ) 11, 401-416 (1960). | Zbl 0099.28103

A.M. Polosuev [12] On the uniformity of the distribution of a system of functions forming the solution of a system of linear finite-difference equations of first order. Dokl. Akad. Nauk SSSR 123, 405-406 (1958). | MR 109147 | Zbl 0088.03804

A.G. Postnikow [13] A criterion for the uniform distribution of an exponential function in the complex domain, Vestn. Leningr. Univ. 13, 81- 88 (1957). | Zbl 0093.05302

A.G. Postnikow [14] A criterion for a completely uniformly distributed sequence, Dokl. Akad. Nauk SSSR 120, 973-975 (1958). | MR 101858 | Zbl 0090.35504

A.G. Postnikow and I.I. Pyateckii [15] Markov-sequence of symbols and continued fractions, Izvest. Akad. Nauk SSSR 21, 729-746 (1957). | MR 101857 | Zbl 0084.13601

I.I. Pyateckii [16] On the distribution functions of the fractional parts of an exponential function, Izvest. Akad. Nauk SSSR 15, 47-52 (1951). | Zbl 0042.04902

A. Rényi [17] Representations for real numbers and their ergodic properties, Acta math. (hung.) 8, 477-493 (1957). | MR 97374 | Zbl 0079.08901

W.A. Rochlin [18] On endomorphisms of compact Abelian groups, Izvest. Akad. Nauk SSSR 13, 329 - 340 (1949).

C. Ryll-Nardzewski [19] On the ergodic theorems II, Studia math. 12, 74-79 (1951). | MR 46583 | Zbl 0044.12401