Lₚ-deviations from zero of polynomials with integral coefficients

• Autorzy: Francisco Luquin
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 69
• Numer: 3
• Strony: 217-228

Daty

wydano

1995

otrzymano

1993-04-20

Twórcy

autor

Francisco Luquin

• Departamento de Matemáticas, Facultad de Ciencias, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain

Bibliografia

• [1] N. I. Achieser, Theory of Approximation, Ungar, New York, 1956.
• [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] 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] 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] E. Aparicio Bernardo, Three theorems on approximation in Lₚ by means of polynomials with integer coefficients, Collect. Math. 28 (1977), 217-234 (in Spanish).
• [6] M. Fekete, Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten, Math. Z. 17 (1923), 228-249.
• [7] L. B. O. Ferguson, Approximation by Polynomials with Integral Coefficients, Math. Surveys 17, Amer. Math. Soc., Providence, R.I., 1980.
• [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] D. Hilbert, Ein Beitrag zur Theorie des Legendre'schen Polynoms, Acta Math. 18 (1894), 155-159.
• [10] I. P. Natanson, Constructive Function Theory, Vols. I, II, Ungar, New York, 1964-1965.
• [11] T. J. Rivlin, The Chebyshev Polynomials, Wiley, New York, 1974.
• [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] W. M. Schmidt, Diophantine Approximation, Lecture Notes in Math. 785, Springer, 1980.
• [14] R. M. Trigub, Approximation of functions by polynomials with integral coefficients, Izv. Akad. Nauk SSSR Ser. Mat. 26 (1962), 261-280 (in Russian)