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Discretization of prime counting functions, convexity and the Riemann hypothesis

Emre Alkan (2023)

Czechoslovak Mathematical Journal

We study tails of prime counting functions. Our approach leads to representations with a main term and an error term for the asymptotic size of each tail. It is further shown that the main term is of a specific shape and can be written discretely as a sum involving probabilities of certain events belonging to a perturbed binomial distribution. The limitations of the error term in our representation give us equivalent conditions for various forms of the Riemann hypothesis, for classical type zero-free...

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