Lₚ-deviations from zero of polynomials with integral coefficients

Francisco Luquin

Acta Arithmetica (1995)

  • Volume: 69, Issue: 3, page 217-228
  • ISSN: 0065-1036

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Francisco Luquin. "Lₚ-deviations from zero of polynomials with integral coefficients." Acta Arithmetica 69.3 (1995): 217-228. <http://eudml.org/doc/206684>.

@article{FranciscoLuquin1995,
author = {Francisco Luquin},
journal = {Acta Arithmetica},
keywords = {-deviations; polynomials with integral coefficients; Diophantine approximation; JFM 25.0817.02; JFM 49.0047.01},
language = {eng},
number = {3},
pages = {217-228},
title = {Lₚ-deviations from zero of polynomials with integral coefficients},
url = {http://eudml.org/doc/206684},
volume = {69},
year = {1995},
}

TY - JOUR
AU - Francisco Luquin
TI - Lₚ-deviations from zero of polynomials with integral coefficients
JO - Acta Arithmetica
PY - 1995
VL - 69
IS - 3
SP - 217
EP - 228
LA - eng
KW - -deviations; polynomials with integral coefficients; Diophantine approximation; JFM 25.0817.02; JFM 49.0047.01
UR - http://eudml.org/doc/206684
ER -

References

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  1. [1] N. I. Achieser, Theory of Approximation, Ungar, New York, 1956. 
  2. [2] E. Aparicio Bernardo, On some properties of polynomials with integer coefficients, and on approximation of functions in the mean by polynomials with integer coefficients, Izv. Akad. Nauk SSSR Ser. Mat. 19 (1955), 303-318 (in Russian). 
  3. [3] E. Aparicio Bernardo, Método de las formas lineales para la acotación de las desviaciones mínimas a cero de los polinomios generalizados de coeficientes enteros, in: Proc. 1st Conference of Portuguese and Spanish Mathematicians (Lisbon, 1972), Inst. 'Jorge Juan' Mat., Madrid, 1973, 133-143. 
  4. [4] E. Aparicio Bernardo, Generalization of a theorem of M. Fekete to polynomials with integer coefficients in several unknowns, Rev. Mat. Hisp.-Amer. (4) 36 (1976), 105-124 (in Spanish). 
  5. [5] E. Aparicio Bernardo, Three theorems on approximation in Lₚ by means of polynomials with integer coefficients, Collect. Math. 28 (1977), 217-234 (in Spanish). Zbl0417.41008
  6. [6] M. Fekete, Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten, Math. Z. 17 (1923), 228-249. 
  7. [7] L. B. O. Ferguson, Approximation by Polynomials with Integral Coefficients, Math. Surveys 17, Amer. Math. Soc., Providence, R.I., 1980. Zbl0441.41003
  8. [8] A. O. Gel'fond, On uniform approximation by polynomials with rational integral coefficients, Uspekhi Mat. Nauk (N.S.) 10 (1) (63) (1955), 41-65 (in Russian). 
  9. [9] D. Hilbert, Ein Beitrag zur Theorie des Legendre'schen Polynoms, Acta Math. 18 (1894), 155-159. 
  10. [10] I. P. Natanson, Constructive Function Theory, Vols. I, II, Ungar, New York, 1964-1965. 
  11. [11] T. J. Rivlin, The Chebyshev Polynomials, Wiley, New York, 1974. Zbl0299.41015
  12. [12] I. N. Sanov, Functions with integral parameters, deviating the least from zero, Leningrad. Gos. Univ. Uchen. Zap. Ser. Mat. Nauk 111 (1949), 32-46 (in Russian). 
  13. [13] W. M. Schmidt, Diophantine Approximation, Lecture Notes in Math. 785, Springer, 1980. Zbl0421.10019
  14. [14] R. M. Trigub, Approximation of functions by polynomials with integral coefficients, Izv. Akad. Nauk SSSR Ser. Mat. 26 (1962), 261-280 (in Russian) Zbl0145.29202

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