论文信息 - An effective lower bound for the height of algebraic numbers - 字舞流文

An effective lower bound for the height of algebraic numbers

We prove that if $\alpha$ is a non-zero algebraic number of degree $d \geq 2$ which is not a root of unity, then $dh(\alpha)>(1/4) (\log(\log (d))/\log(d))^3.

Paul Voutier | P. Voutier

[1] Andrzej Schinzel,et al. A refinement of two theorems of Kronecker. , 1965 .

[2] Hugh L. Montgomery,et al. Algebraic integers near the unit circle , 1971 .

[3] D. H. Lehmer. Factorization of Certain Cyclotomic Functions , 1933 .

[4] E. Straus,et al. On a conjecture of D. H. Lehmer , 1982 .

[5] David W. Boyd,et al. Reciprocal polynomials having small measure. II , 1980 .

[6] J. Rosser,et al. Approximate formulas for some functions of prime numbers , 1962 .

[7] C. Stewart. Algebraic integers whose conjugates lie near the unit circle , 1978 .

[8] G. Robin. Estimation de la fonction de Tchebychef θ sur le k-ième nombre premier et grandes valeurs de la fonction ω(n) nombre de diviseurs premiers de n , 1983 .

[9] A. Dubickas. On a conjecture of A. Schinzel and H. Zassenhaus , 1993 .

[10] Michel Laurent,et al. Formes linéaires en deux logarithmes et déterminants d′interpolation , 1995 .

[11] M. Bertin,et al. Conjecture de Lehmer et petits nombres de Salem , 1989 .

[12] A. Bazylewicz,et al. On the product of the conjugates outside the unit circle of an algebraic integer , 1976 .

[13] Edward Dobrowolski,et al. On a question of Lehmer and the number of irreducible factors of a polynomial , 1979 .