Revista de la
Unión Matemática Argentina
On the zeros of univariate E-polynomials
María Laura Barbagallo, Gabriela Jeronimo, and Juan Sabia
Volume 65, no. 1 (2023), pp. 33–46

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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.


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