An improvement of the Erdos-Turan theorem on the distribution of zeros of polynomials Academic Article uri icon


  • We prove a subtle 'one-sided' improvement of a classical result of P. Erdo{combining double acute accent}s and P. Turn on the distribution of zeros of polynomials. The proof of this improvement is quite short and rather elementary. Nevertheless it allows us to obtain a beautiful recent result of V. Totik and P. Varj as a simple corollary, and in a somewhat stronger form, without any use of a potential theoretic machinery. Namely, if the modulus of a monic polynomial P of degree n (with complex coefficients) on the unit circle of the complex plane is at most 1 + o (1) uniformly, then the multiplicity of each zero of P on the unit circle is o (n1 / 2). Our approach is based on the interesting observation that the Erdo{combining double acute accent}s-Turn Theorem improves itself. To cite this article: T. Erdlyi, C. R. Acad. Sci. Paris, Ser. I 346 (2008). 2008 Acadmie des sciences.

published proceedings


author list (cited authors)

  • Erdelyi, T.

citation count

  • 15

complete list of authors

  • Erdélyi, Tamás

publication date

  • March 2008