On the distribution on the roots of polynomials

Francesco Amoroso; Maurice Mignotte

Annales de l'institut Fourier (1996)

  • Volume: 46, Issue: 5, page 1275-1291
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Amoroso, Francesco, and Mignotte, Maurice. "On the distribution on the roots of polynomials." Annales de l'institut Fourier 46.5 (1996): 1275-1291. <http://eudml.org/doc/75212>.

@article{Amoroso1996,
abstract = {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.},
author = {Amoroso, Francesco, Mignotte, Maurice},
journal = {Annales de l'institut Fourier},
keywords = {polynomials; roots; equidistribution; conjugate harmonic functions; theorem of Erdös–Turán},
language = {eng},
number = {5},
pages = {1275-1291},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the distribution on the roots of polynomials},
url = {http://eudml.org/doc/75212},
volume = {46},
year = {1996},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 46
IS - 5
SP - 1275
EP - 1291
AB - 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.
LA - eng
KW - polynomials; roots; equidistribution; conjugate harmonic functions; theorem of Erdös–Turán
UR - http://eudml.org/doc/75212
ER -

References

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  1. [A] F. AMOROSO, Algebraic numbers close to 1 and variants of Mahler's measure, Journal of Number Theory, 60 (1996), 80-96. Zbl0866.11060MR97g:11075
  2. [B] H.-P. BLATT, On the distribution of simple zeros of polynomials, Journal of Approximation Theory, 69 (1992), 250-268. Zbl0757.41011MR93h:41009
  3. [Ba] A. BAERNSTEIN, Some sharp inequalities for conjugate functions, Indiana Univ. Math. J., 27 (1978), 833-852. Zbl0372.42007MR80g:30022
  4. [D] B. DAVIS, On the weak type (1, 1) inequality for conjugate functions, Proc. Amer. Math. Soc., 44 (1974), 307-311. Zbl0259.42016MR50 #879
  5. [ET] P. ERDÖS and P. TURÁN, On the distribution of roots of polynomials, Annals of Math., 51 (1950), 105-119. Zbl0036.01501MR11,431b
  6. [G] T. GANELIUS, Sequences of analytic functions and their zeros, Arkiv. för Matematik, 3 (14958), 1-50. Zbl0055.06905MR16,23c
  7. [K] P. KOOSIS, Introduction to Hp spaces, Cambridge, London, 1980. Zbl0435.30001
  8. [M] M. MIGNOTTE, Remarque sur une question relative à des fonctions conjuguées, C.R. Acad. Sci. Paris, t. 315, Série I, (1992) 907-911. Zbl0773.31002MR93i:30007
  9. [T] V. TOTIK, Distribution of simple zeros of polynomials, Acta Math., 170 (1993), 1-28. Zbl0888.41003MR95i:41011

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