On the number of polynomials of small house
Let \(\varepsilon \) be a positive number and \(d\) be a sufficiently large positive integer. The author proves that the number of monic integer polynomials of degree \(d\) with integer coefficients whose roots are of moduli \({}\leq d^{\varepsilon /d}\) is less than \(\exp(d^{2/3+\varepsilon })\). This improves on previous results. Of course, this study is related with Lehmer's problem on Mahler measure.
scientific article; zbMATH DE number 1466098