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math.NT2022
RH-Dependent Estimates of Remainder in Modified Mertens Formula
Gennadiy Kalyabin
Assuming the validity of Riemann Hypothesis (RH), we derive the explicit bilateral estimates ("narrow passage") of the remainder in the modified Mertens asymptotic formula for the…
math.NT2022
Remainder in Modified Mertens Formula and Ramanujan Inequality
Gennadiy Kalyabin
A highly strong upper estimate in the modified asymptotic formula for sums of the primes' reciprocals is proved to be necessary (as well as sufficient) in order the Ramanujan inequ…