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Title: | El teorema d’Erdős-Turán |
Author: | Sánchez Garcés, Ana |
Director/Tutor: | Marzo Sánchez, Jordi |
Keywords: | Teoria geomètrica de funcions Treballs de fi de grau Funcions de variables complexes Polinomis Geometric function theory Bachelor's theses Functions of complex variables Polynomials |
Issue Date: | 13-Jun-2022 |
Abstract: | [en] A classical result of Erdős and Turán states that if a monic polynomial has small size on the unit circle and its constant coefficient is not too small, then its zeros cluster near the unit circle and become equidistributed in angle. The theorem of Erdős and Turán are then two results: that the zeros of a polynomial lie close to the unit circle and that the angles of the zeros are well distributed. The first result (Theorem 1 p.4) is a simple consequence of Jensen’s formula. The second (Theorem 2 p.5), which is the main result of the paper, we will prove by seeing that the discrepancy of the angles of the zeros of a polynomial is bounded by a measure of the size of the polynomial at the circle. To prove these results we will follow the article by K. Soundararajan [14]. |
Note: | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Jordi Marzo Sánchez |
URI: | http://hdl.handle.net/2445/196763 |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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tfg_sanchez_garces_ana.pdf | Memòria | 615.31 kB | Adobe PDF | View/Open |
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