I am trying to calculate the inverse Laplace transform of a probability distribution, and while I don't believe I can get a closed form expression, I would like to get an idea of the general shape of the distribution. The Laplace transform is a nice rational function, however, the roots of the denominator are the inverse (I mean $1/z$) of the following $$\frac{z^n-1}{z-1}=b$$
where $b>1$ and real. What can be said about the zeros of the polynomial? Are they all real, what is their degeneracy? Are there any $b$ derived bounds on the roots (i.e. do they all fall in a circle of radius $2b^{1/n}$ for example-- I know it is not true, just giving an example)?