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On the product of heights of algebraic numbers summing to real numbers

J. Garza; M. I. M. Ishak; C. Pinner — 2010

Acta Arithmetica

Heights of roots of polynomials with odd coefficients

J. Garza; M. I. M. Ishak; M. J. Mossinghoff; C. G. Pinner; B. Wiles — 2010

Journal de Théorie des Nombres de Bordeaux

Let $α$ be a zero of a polynomial of degree $n$ with odd coefficients, with $α$ not a root of unity. We show that the height of $α$ satisfies $h (α) \geq \frac{0.4278}{n + 1} .$ More generally, we obtain bounds when the coefficients are all congruent to $1$ modulo $m$ for some $m \geq 2$ .

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