V. Flammang, G. Rhin and C. J. Smyth, The integer transfinite diameter of intervals and totally real algebraic integers, J. Theor. Nombres Bordeaux 9 (1997), 137-168. Home/Search Document Not in Database Summary Related Articles Check |
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Small Polynomials With Integer Coefficients - Pritsker (Correct)
....of Aparicio (1.19) 1.21) # 1 # 0.26, and used this to show that the strict inequality holds in (1. 18) Hence the Gorshkov polynomials do not give the exact value of t Z ( 0, 1] The ideas of Borwein and Erdelyi have been developed in the papers by Flammang [13] by Flammang, Rhin and Smyth [14], and by Habsieger and Salvy [18] to obtain further numerical improvements in the upper bounds for t Z on [0, 1] and on Farey intervals. In particular, Habsieger and Salvy computed 75 first integer Chebyshev polynomials for [0, 1] and found the best known upper bound (1.23) t Z ( 0, 1] # ....
....to obtain further numerical improvements in the upper bounds for t Z on [0, 1] and on Farey intervals. In particular, Habsieger and Salvy computed 75 first integer Chebyshev polynomials for [0, 1] and found the best known upper bound (1.23) t Z ( 0, 1] # 0.42347945. Flammang, Rhin and Smyth [14] generalized the approach of [5] to improve the lower bounds in (1.21) # 1 # 0.264151, # 2 # 0.021963 and # 3 # 0.005285, as well as bounds for six additional factors of the integer Chebyshev polynomials on [0, 1] They also extended the Gorshkov polynomials technique to the Farey intervals ....
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V. Flammang, G. Rhin and C. J. Smyth, The integer transfinite diameter of intervals and totally real algebraic integers, J. Theor. Nombres Bordeaux 9 (1997), 137-168.
Chebyshev Polynomials With Integer Coefficients - Pritsker (Correct)
.... Gamma x) ff 1 n] 2x Gamma 1) ff 2 n] 5x 2 Gamma 5x 1) ff 3 n] R n (x) as n 1; 2.2) where ff 1 0:1456; ff 2 0:0166 and ff 3 0:0037; 2.3) and R n 2 P n (Z) n 2 N. Borwein and Erd elyi proved that ff 1 0:26 (2.4) in (2.2) see Theorem 3. 1 of [3] Flammang, Rhin and Smyth [8] recently generalized the ideas of [3] and obtained the following lower bounds ff 1 0:264151; ff 2 0:021963 and ff 3 0:005285: 2.5) They also considered six additional factors of Q n (x) and studied other intervals (cf. 8] for the details) We use the methods of the weighted potential ....
....0:26 (2.4) in (2.2) see Theorem 3.1 of [3] Flammang, Rhin and Smyth [8] recently generalized the ideas of [3] and obtained the following lower bounds ff 1 0:264151; ff 2 0:021963 and ff 3 0:005285: 2. 5) They also considered six additional factors of Q n (x) and studied other intervals (cf. [8] for the details) We use the methods of the weighted potential theory, developed during the last two decades, to study the integer Chebyshev problem and to improve CHEBYSHEV POLYNOMIALS WITH INTEGER COEFFICIENTS 5 the bounds for ff 1 and ff 2 . A complete account on the weighted potential ....
[Article contains additional citation context not shown here]
V. Flammang, G. Rhin and C. J. Smyth, The integer transfinite diameter of intervals and totally real algebraic integers, J. Th'eor. Nombres Bordeaux 9 (1997), 137-168.
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