On a result of Mahler on the decimal expansions of (nα)

• Autorzy: Daniel Berend , Michael D. Boshernitzan
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1994
• Tom: 66
• Numer: 4
• Strony: 315-322

Daty

wydano

1994

otrzymano

1992-08-10

Twórcy

autor

Daniel Berend

• Department of Mathematics and Computer Science, Ben-Gurion University, Beer-Sheva 84105, Israel

autor

Michael D. Boshernitzan

• Department of Mathematics, Rice University, Houston, Texas 77251, U.S.A.

Bibliografia

• [AP] N. Alon and Y. Peres, Uniform dilations, J. Geom. Funct. Anal. 2 (1992), 1-28.
• [B] M. Boshernitzan, Uniform distribution and Hardy fields, J. Analyse Math., to appear.
• [C] J. R. Chen, On Professor Hua's estimate of exponential sums , Sci. Sinica 20 (1977), 711-719.
• [G] S. Glasner, Almost periodic sets and measures on the torus, Israel J. Math. 32 (1979), 161-172.
• [H] L. K. Hua, Introduction to Number Theory, Springer, New York, 1982.
• [KN] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York, 1974.
• [M] K. Mahler, Arithmetical properties of the digits of the multiples of an irrational number, Bull. Austral. Math. Soc. 8 (1973), 191-203.
• [S] S. B. Stečkin, An estimate of a complete rational trigonometric sum, Analytic Number Theory, Mathematical Analysis and their Applications, Trudy Mat. Inst. Steklov. 143 (1977), 188-207, 211; English transl.: Proc. Steklov Inst. Math. (1980), 201-220.
• [W] H. Weyl, Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), 313-352.