On the relations between the zeros of a polynomial and its Mahler measure
Copyright policy )On the relations between the zeros of a polynomial and its Mahler measure
In this work, we are dealing with some properties relating the zeros of a polynomial and its Mahler measure. We provide estimates on the number of real zeros of a polynomial, lower bounds on the distance between the zeros of a polynomial and non-zeros located on the unit circle and a lower bound on the number of zeros of a polynomial in the disk $\{\vert x-1\vert<1\}$.
Mathematics - Number Theory, Polynomials in real and complex fields: location of zeros (algebraic theorems), estimation of the zeros, Integer polynomials, PV-numbers and generalizations; other special algebraic numbers; Mahler measure, Mahler measure, FOS: Mathematics, Number Theory (math.NT), 11C08 11R06, 11C08, 12D10, Algebraic numbers; rings of algebraic integers, Polynomials in number theory, Polynomials (irreducibility, etc.), length of a polynomial, number of real zeros, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]
Mathematics - Number Theory, Polynomials in real and complex fields: location of zeros (algebraic theorems), estimation of the zeros, Integer polynomials, PV-numbers and generalizations; other special algebraic numbers; Mahler measure, Mahler measure, FOS: Mathematics, Number Theory (math.NT), 11C08 11R06, 11C08, 12D10, Algebraic numbers; rings of algebraic integers, Polynomials in number theory, Polynomials (irreducibility, etc.), length of a polynomial, number of real zeros, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]
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