P. Turán asked if there exists an absolute constant C such that for every polynomial f ∈ ℤ[x] there exists an irreducible polynomial g ∈ ℤ[x] with deg(g) ≤ deg(f) and L(f — g) ≤ C, where L(·) denotes ...

We define a power compositional sextic polynomial to be a monic sextic polynomial f(x) := h(xd) ϵ ℤ[x], where h(x) is an irreducible quadratic or cubic polynomial, and d = 3 or d = 2, respectively. In ...

Lie groups, as continuous groups endowed with differentiable structure, provide a powerful framework to study symmetries across mathematics and physics. Their associated representation theory offers ...