Non-monogenity of some number fields generated by binomials or trinomials of prime-power degree

Let q be a prime number and K = Q(theta) be an algebraic number field with theta a root of an irreducible polynomial x(qs )- ax - b having integer coefficients. In this paper, we provide some explicit conditions involving only s,q,a,b for which K is non-monogenic. As an application, in the special case of a = 0 and q = 2, we show that if s >= 2 and 32 divides b - 1, then K is not monogenic. We illustrate our results through examples.