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exponential polynomial; Newton inequality; Newton coefficients; p-Newton sequence

References:

[1] Johnson, C. R., Marijuán, C., Pisonero, M.: **Inequalities for linear combinations of monomials in p-Newton sequences**. Linear Algebra Appl. 439 (2013), 2038-2056. MR 3090453 | Zbl 1305.15022

[2] Johnson, C. R., Marijuán, C., Pisonero, M.: **Matrices and spectra satisfying the Newton inequalities**. Linear Algebra Appl. 430 (2009), 3030-3046. MR 2517856 | Zbl 1189.15009

[3] Johnson, C. R., Marijuán, C., Pisonero, M., Walch, O.: **Monomials inequalities for Newton coefficients and determinantal inequalities for p-Newton matrices**. Trends in Mathematics, Notions of Positivity and the Geometry of Polynomials Springer, Basel Brändén, Petter et al. (2011), 275-282. MR 3051171

[4] Newton, I.: **Arithmetica Universalis: Sive de Compositione et Resolutione Arithmetica Liber**. William Whiston London (1707).

[5] Wang, X.: **A simple proof of Descartes's rule of signs**. Am. Math. Mon. 111 (2004), 525-526. DOI 10.2307/4145072