Superpolynomially Large Support in Every Irreducible Factor of Lacunary Polynomials
We show that there exist infinitely many polynomials $F\in\mathbb{Q}[x]$ with exactly $m$ nonzero coefficients such that every irreducible factor of \(F\) over \(\mathbb{Q}\) has \(\exp\) \(\!\bigl(\Omega(\sqrt{m/\log m})\bigr)\) nonzero coefficients. This places multiplication in a sharply different category from powe...