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math.NT2020
Asymptotic expansions of weighted prime power counting functions
Jesse Elliott
We prove several asymptotic continued fraction expansions of , , , , and related functions, where is the prime counti…
math.GR2020
Group actions, power mean orbit size, and musical scales
Jesse Elliott
We provide an application of the theory of group actions to the study of musical scales. For any group , finite -set , and real number , we define the {\it -power di…
math.NT2020
Harmonic numbers and the prime counting function
Jesse Elliott
We provide approximations to the prime counting function by various discretized versions of the logarithmic integral function, expressed solely in terms of the harmonic numbers. We…