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On a Fekete-Szegö Theorem

Thérèse Fallièro

Abstract

We consider again a classical theorem relating capacities and algebraic integers and the question of the simultaneous approximation of $ n-1$ different complex numbers by conjugate algebraic integers of degree $n$.

On a Fekete-Szegö Theorem

Abstract

We consider again a classical theorem relating capacities and algebraic integers and the question of the simultaneous approximation of different complex numbers by conjugate algebraic integers of degree .

Paper Structure

This paper contains 20 sections, 116 equations.

Table of Contents

  1. Introduction
  2. Definitions
  3. Approximation on intervals
  4. Algebraic integers with all conjugates in a given compact.
  5. Precisions on the properties of $K$
  6. On a compact symmetric with respect to the real axis
  7. The boundary
  8. Hyperelliptic Riemann surface associated to $\Gamma$.
  9. The notion of "calibrated"
  10. A generalization of Serre's method, the case of a compact of ${\mathbb R}$
  11. Some approximations
  12. JACOBI
  13. Demonstration of the theorem following Serre.
  14. Some review of some spectra
  15. The case of the spectrum of a periodic Jacobi matrix
  16. ...and 5 more sections

Theorems & Definitions (9)

  • proof
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