Polynomials with restricted coefficients and prescribed noncyclotomic factors

Abstract: The algorithms described in this paper were developed to investigate three problems regarding polynomials with restricted coefficients: (i) determining whether there exist polynomials with {0,1} coefficients and repeated noncyclotomic factors, (ii) searching for polynomials with {-1,1} coefficients and small Mahler measure, and (iii) finding polynomials with {-1,0,1} coefficients with a root of high multiplicity off the unit circle. The results in the first problem presented here answer a question of Odlyzko and Poonen.