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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.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…