On the distribution on the roots of polynomials
Annales de l'Institut Fourier, Tome 46 (1996) no. 5, pp. 1275-1291.

Grâce à des résultats classiques sur les fonctions conjuguées, nous donnons des démonstrations très courtes des théorèmes d’Erdös–Turán et de Blatt sur la distribution angulaire des racines des polynômes. Puis nous étudions quelques exemples.

Using classical results on conjugate functions, we give very short proofs of theorems of Erdös–Turán and Blatt concerning the angular distribution of the roots of polynomials. Then we study some examples.

@article{AIF_1996__46_5_1275_0,
     author = {Amoroso, Francesco and Mignotte, Maurice},
     title = {On the distribution on the roots of polynomials},
     journal = {Annales de l'Institut Fourier},
     pages = {1275--1291},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {46},
     number = {5},
     year = {1996},
     doi = {10.5802/aif.1548},
     zbl = {0867.26009},
     mrnumber = {1427125},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1548/}
}
TY  - JOUR
AU  - Amoroso, Francesco
AU  - Mignotte, Maurice
TI  - On the distribution on the roots of polynomials
JO  - Annales de l'Institut Fourier
PY  - 1996
SP  - 1275
EP  - 1291
VL  - 46
IS  - 5
PB  - Association des Annales de l’institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.1548/
DO  - 10.5802/aif.1548
LA  - en
ID  - AIF_1996__46_5_1275_0
ER  - 
%0 Journal Article
%A Amoroso, Francesco
%A Mignotte, Maurice
%T On the distribution on the roots of polynomials
%J Annales de l'Institut Fourier
%D 1996
%P 1275-1291
%V 46
%N 5
%I Association des Annales de l’institut Fourier
%U http://www.numdam.org/articles/10.5802/aif.1548/
%R 10.5802/aif.1548
%G en
%F AIF_1996__46_5_1275_0
Amoroso, Francesco; Mignotte, Maurice. On the distribution on the roots of polynomials. Annales de l'Institut Fourier, Tome 46 (1996) no. 5, pp. 1275-1291. doi : 10.5802/aif.1548. http://www.numdam.org/articles/10.5802/aif.1548/

[A] F. Amoroso, Algebraic numbers close to 1 and variants of Mahler's measure, Journal of Number Theory, 60 (1996), 80-96. | MR | Zbl

[B] H.-P. Blatt, On the distribution of simple zeros of polynomials, Journal of Approximation Theory, 69 (1992), 250-268. | MR | Zbl

[Ba] A. Baernstein, Some sharp inequalities for conjugate functions, Indiana Univ. Math. J., 27 (1978), 833-852. | MR | Zbl

[D] B. Davis, On the weak type (1, 1) inequality for conjugate functions, Proc. Amer. Math. Soc., 44 (1974), 307-311. | MR | Zbl

[ET] P. Erdös and P. Turán, On the distribution of roots of polynomials, Annals of Math., 51 (1950), 105-119. | MR | Zbl

[G] T. Ganelius, Sequences of analytic functions and their zeros, Arkiv. för Matematik, 3 (14958), 1-50. | MR | Zbl

[K] P. Koosis, Introduction to Hp spaces, Cambridge, London, 1980. | MR | Zbl

[M] M. Mignotte, Remarque sur une question relative à des fonctions conjuguées, C.R. Acad. Sci. Paris, t. 315, Série I, (1992) 907-911. | MR | Zbl

[T] V. Totik, Distribution of simple zeros of polynomials, Acta Math., 170 (1993), 1-28. | MR | Zbl

Cité par Sources :