Thread by @LGcommaI

#ConradMitzenmacher-6
"In this paper, we begin by reviewing the fascinating history of this fundamental problem. Then, we use methods from #ComplexAnalysis to prove that Miller’s random monkey experiment yields power laws for [the] rank-frequency distribution
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>with probability assignments to keys satisfying a rationality assumption on log-ratios of pairs of probabilities.
We use analytic methods to establish a simple explicit power law in cases with rational log-ratios for pairs of probabilities; more specifically,
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>we use generalized Dirichlet series and an elementary identity established by means of Fourier series. Passing to a limit on these formulas predicts an analogous result in the remaining “irrational” cases, and this prediction agrees with an unpublished theorem..by Montgomery;
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>in Section VI, we provide Montgomery’s argument, that uses methods that are standard in analytic number theory.
The use of analytic techniques to study problems of this type is not in itself novel (see [8]–[10], for example), and it is also a well-known phenomenon that
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>rationality issues can lead to cases that behave in a manner somewhat different from generic cases.
The novelty of this paper is, therefore, not in the consideration of analytic techniques but rather in the application of these techniques to an interesting nontrivial problem
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