On the zeros of univariate E-polynomials

BARBAGALLO, MARÍA LAURA; JERONIMO, GABRIELA; SABIA, JUAN

REVISTA DE LA UNIóN MATEMáTICA ARGENTINA

UNION MATEMATICA ARGENTINA

Lugar: Bahia Blanca; Año: 2023 vol. 65 p. 33 - 46

0041-6932

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.