On distribution functions of ξ(3/2)ⁿ mod 1

Oto Strauch

Acta Arithmetica (1997)

  • Volume: 81, Issue: 1, page 25-35
  • ISSN: 0065-1036

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Oto Strauch. "On distribution functions of ξ(3/2)ⁿ mod 1." Acta Arithmetica 81.1 (1997): 25-35. <http://eudml.org/doc/207052>.

@article{OtoStrauch1997,
author = {Oto Strauch},
journal = {Acta Arithmetica},
keywords = {uniform distribution modulo 1; distribution function; functional equation},
language = {eng},
number = {1},
pages = {25-35},
title = {On distribution functions of ξ(3/2)ⁿ mod 1},
url = {http://eudml.org/doc/207052},
volume = {81},
year = {1997},
}

TY - JOUR
AU - Oto Strauch
TI - On distribution functions of ξ(3/2)ⁿ mod 1
JO - Acta Arithmetica
PY - 1997
VL - 81
IS - 1
SP - 25
EP - 35
LA - eng
KW - uniform distribution modulo 1; distribution function; functional equation
UR - http://eudml.org/doc/207052
ER -

References

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  1. [1] M. Bennett, Fractional parts of powers of rational numbers, Math. Proc. Cambridge Philos. Soc. 114 (1993), 191-201. Zbl0791.11030
  2. [2] G. Choquet, Construction effective de suites (k(3/2)ⁿ). Étude des mesures (3/2)-stables, C. R. Acad. Sci. Paris Sér. A-B 291 (1980), A69-A74 (MR 82h:10062a-d). Zbl0443.10035
  3. [3] L. Flatto, J. C. Lagarias and A. D. Pollington, On the range of fractional parts {ξ(p/q)ⁿ}, Acta Arith. 70 (1995), 125-147. Zbl0821.11038
  4. [4] H. Helson and J.-P. Kahane, A Fourier method in diophantine problems, J. Analyse Math. 15 (1965), 245-262 (MR 31#5856). Zbl0135.10804
  5. [5] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York, 1974. Zbl0281.10001
  6. [6] K. Mahler, An unsolved problem on the powers of 3/2, J. Austral. Math. Soc. 8 (1968), 313-321 (MR 37#2694). Zbl0155.09501
  7. [7] I. I. Piatetski-Shapiro, On the laws of distribution of the fractional parts of an exponential function, Izv. Akad. Nauk SSSR Ser. Mat. 15 (1951), 47-52 (MR 13, 213d) (in Russian). Zbl0042.04902
  8. [8] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361-375. Zbl0089.04002
  9. [9] R. Tijdeman, Note on Mahler's 3/2-problem, Norske Vid. Selsk. Skr. 16 (1972), 1-4. Zbl0227.10025
  10. [10] J. G. van der Corput, Verteilungsfunktionen I-VIII, Proc. Akad. Amsterdam 38 (1935), 813-821, 1058-1066; 39 (1936), 10-19, 19-26, 149-153, 339-344, 489-494, 579-590. 
  11. [11] T. Vijayaraghavan, On the fractional parts of the powers of a number, I, J. London Math. Soc. 15 (1940), 159-160. 

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