Dirichlet Polynomials and Entropy.

A Dirichlet polynomial in one variable y is a function of the form d(y)=anny+⋯+a22y+a11y+a00y for some n,a0,…,an∈N. We will show how to think of a Dirichlet polynomial as a set-theoretic bundle, and thus as an empirical distribution. We can then consider the Shannon entropy H(d) of the corresponding probability distribution, and we define its (or, classically, its ) by L(d)=2H(d).