On the zeros of univariate E-polynomials

María Laura Barbagallo ^[1] ; Gabriela Jerónimo ^[1] ; Juan Sabia ^[1]
1. [1] Universidad de Buenos Aires
  
  Universidad de Buenos Aires
  
  Argentina
Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 65, Nº. 1, 2023, págs. 33-46
Idioma: inglés
DOI: 10.33044/revuma.2305
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Resumen
- We consider two problems concerning real zeros of univariate E-polynomials. First, we prove an explicit upper bound for the absolute values of the zeroes of an E-polynomial defined by polynomials with integer coefficients that improves the bounds known up to now. On the other hand, we extend the classical Budan–Fourier theorem for real polynomials to E-polynomials. This result gives, in particular, an upper bound for the number of real zeroes of an E-polynomial. We show this bound is sharp for particular families of these functions, which proves that a conjecture by D. Richardson is false.