Dirichlet Polynomials and Entropy

@article{Spivak2021DirichletPA,
  title={Dirichlet Polynomials and Entropy},
  author={David I. Spivak and Timothy Hosgood},
  journal={Entropy},
  year={2021},
  volume={23}
}
A Dirichlet polynomial d 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 length (or, classically, its perplexity) by L(d)=2H(d). On the other hand, we will define a rig homomorphism h:Dir→Rect from the rig of Dirichlet… 
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