RH-Dependent Estimates of Remainder in Modified Mertens Formula
Gennadiy Kalyabin
TL;DR
This paper derives explicit bilateral estimates for the remainder in a modified Mertens formula assuming RH, providing new criteria for the Riemann Hypothesis based on these estimates.
Contribution
It introduces reversible bilateral estimates of the remainder in the modified Mertens formula under RH, offering novel criteria for the Riemann Hypothesis.
Findings
Explicit bilateral estimates of the remainder in the modified Mertens formula.
Reversible estimates that lead to new RH criteria.
Potential implications for testing the Riemann Hypothesis.
Abstract
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 sums of primes' reciprocals. These results are reversable, thus yielding some new criteria for RH.
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Taxonomy
TopicsAnalytic Number Theory Research · Advanced Algebra and Geometry · Meromorphic and Entire Functions