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arXiv · 2201.02663

Remainder in Modified Mertens Formula and Ramanujan Inequality

Gennadiy Kalyabin
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Abstract

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 inequality holds true. Some other criteria in similar terms are also obtained.

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Gennadiy Kalyabin. 2022-01-07. Remainder in Modified Mertens Formula and Ramanujan Inequality. https://arxiv.org/abs/2201.02663

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