On the discrepancy estimate of normal numbers

M. B. Levin

Acta Arithmetica (1999)

  • Volume: 88, Issue: 2, page 99-111
  • ISSN: 0065-1036

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M. B. Levin. "On the discrepancy estimate of normal numbers." Acta Arithmetica 88.2 (1999): 99-111. <http://eudml.org/doc/207240>.

@article{M1999,
author = {M. B. Levin},
journal = {Acta Arithmetica},
keywords = {Korobov's problem; van der Corput-type sequences; normal numbers; discrepancy},
language = {eng},
number = {2},
pages = {99-111},
title = {On the discrepancy estimate of normal numbers},
url = {http://eudml.org/doc/207240},
volume = {88},
year = {1999},
}

TY - JOUR
AU - M. B. Levin
TI - On the discrepancy estimate of normal numbers
JO - Acta Arithmetica
PY - 1999
VL - 88
IS - 2
SP - 99
EP - 111
LA - eng
KW - Korobov's problem; van der Corput-type sequences; normal numbers; discrepancy
UR - http://eudml.org/doc/207240
ER -

References

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  1. [B] R. Bejian, Sur certaines suites présentant une faible discrépance à l'origine, C. R. Acad. Sci. Paris Sér. A 286 (1978), 135-138. Zbl0378.10031
  2. [BH] M. Bicknell and V. E. Hoggart, Jr., Unit determinants in generalized Pascal triangles, Fibonacci Quart. 11 (1978), 131-144. 
  3. [F] H. Faure, Discrépance de suites associées à un système de numération (en dimension s), Acta Arith. 41 (1982), 337-351. Zbl0442.10035
  4. [G] I. S. Gal and L. Gal, The discrepancy of the sequence ( 2 n x ) , Indag. Math. 26 (1964), 129-143. Zbl0152.03603
  5. [K1] N. M. Korobov, Numbers with bounded quotient and their applications to questions of Diophantine approximation, Izv. Akad. Nauk SSSR Ser. Mat. 19 (1955), 361-380. 
  6. [K2] N. M. Korobov, Distribution of fractional parts of exponential function, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 21 (1966), no. 4, 42-46. 
  7. [L1] M. B. Levin, The distribution of fractional parts of the exponential function, Soviet Math. (Izv. VUZ) 21 (1977), no. 11, 41-47. 
  8. [L2] M. B. Levin, On the upper bounds of discrepancy of completely uniform distributed and normal sequences, AMS-IMU joint meeting, Jerusalem, Israel, May 24-26, 1995, Abstracts Amer. Math. Soc. 16 (1995), 556-557. 
  9. [N] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, CBMS-NSF Regional Conf. Ser. in Appl. Math. 63, Philadelphia, 1992. 
  10. [P] V. N. Popov, Asymptotic formula for the sum of sums of the elements of the continued fractions for numbers of the form a/p, J. Soviet Math. 17 (1981), 2137-2147. Zbl0466.10004
  11. [Po] A. G. Postnikov, Arithmetic modeling of random processes, Proc. Steklov Inst. Math. 57 (1960). 
  12. [S] J. Schiffer, Discrepancy of normal numbers, Acta Arith. 47 (1986), 175-186. Zbl0556.10036
  13. [So] I. M. Sobol', Multidimensional Quadrature Formulas and Haar Functions, Nauka, Moscow, 1969 (in Russian). Zbl0195.16903

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