Auxiliary Polynomials for Some Problems regarding Mahler’s Measure
نویسندگان
چکیده
We describe an iterative method of constructing some favorable auxiliary polynomials used to obtain lower bounds in some problems of algebraic number theory. With this method we improve a lower bound on Mahler’s measure of a polynomial with no cyclotomic factors whose coefficients are all congruent to 1 modulo m for some integer m ≥ 2, raise a lower bound in the problem of Schinzel and Zassenhaus on the largest root of such a polynomial, and improve a lower bound on the absolute Weil height of an algebraic unit whose minimal polynomial splits completely over a p-adic field.
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