On integer Chebyshev polynomials

Abstract

We are concerned with the problem of minimizing the supremum norm on [ 0 , 1 ] \lbrack 0,1\rbrack of a nonzero polynomial of degree at most n n with integer coefficients. We use the structure of such polynomials to derive an efficient algorithm for computing them. We give a table of these polynomials for degree up to 75 75 and use a value from this table to answer an open problem due to P. Borwein and T. Erdélyi and improve a lower bound due to Flammang et al.