We are concerned with the problem of minimizing the supremum norm on of a nonzero polynomial of degree at most n with integer coefficients. We use the structure of such polynomials to derive an efficient algorithm for computing them.
Introduction Let d n denote the lowest common multiple of .
This method may be refined as follows. Much is known about these polynomials and their asymptotic structure. Therefore one cannot prove the prime number theorem in this way. In this paper, we first prove two lemmas that halve the degree of the polynomials we need to look for. This step enables us to compute polynomials of larger degree but we cannot guarantee to find them all anymore.