V. Flammang, Sur le diam`etre transfini entier d'un intervalle `a extr'emit'es rationnelles, Ann. Inst. Fourier Gren. 45 (1995), 779793. Home/Search Document Not in Database Summary Related Articles Check |
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Chebyshev Polynomials With Integer Coefficients - Pritsker (Correct)
....optimization techniques. Although this is by no means straightforward, both theoretically and practically, this nevertheless becomes more accessible for computations with growing power of modern computers. Thus, the upper bound in (1. 7) has recently been improved several times (cf. 3] 6] [7] and [9] The value in (1.7) is taken from [9] and to our knowledge is the best computed upper bound. 4 IGOR E. PRITSKER 2. Asymptotic structure of the integer Chebyshev polynomials We are interested in the asymptotic structure of the polynomials Q n 2 P n (Z) satisfying kQ n k [0;1] inf ....
V. Flammang, Sur le diam`etre transfini entier d'un intervalle `a extr'emit'es rationnelles, Ann. Inst. Fourier Gren. 45 (1995), 779793.
The Integer Chebyshev Problem - Borwein, Erdélyi (1995) (4 citations) (Correct)
....2; n) 1=n e, by the prime number theorem and it follows that Omega Gammah ; 1] 1=e: 3 This is not however the right lower bound. The best previous bounds known on [0; 1] give (1. 9) 1 (2:37686 : Omega Gamma2 ; 1] 1 (2:3541 : See Aparicio [2,3,4,5] Amoroso [1], and the references therein. The upper bound is in Amoroso [1] example. The lower bound is based on a method attributed to a number of people and variously rediscovered. Aparicio [3] attributes it to Gorshkov. It amounts to, in our context, showing that for every fixed pn 2 Zn there exist ....
....it follows that Omega Gammah ; 1] 1=e: 3 This is not however the right lower bound. The best previous bounds known on [0; 1] give (1.9) 1 (2:37686 : Omega Gamma2 ; 1] 1 (2:3541 : See Aparicio [2,3,4,5] Amoroso [1] and the references therein. The upper bound is in Amoroso [1]. example. The lower bound is based on a method attributed to a number of people and variously rediscovered. Aparicio [3] attributes it to Gorshkov. It amounts to, in our context, showing that for every fixed pn 2 Zn there exist infinitely many polynomials q k 2 Znk with no common factors with ....
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F. Amoroso, Sur le diam`etre transfini entier d'un intervalle r'eel, Ann. Inst. Fourier, Grenoble 40 (1990), 885--911. 22
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