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Consequences of Invariant Functions for the Riemann Hypothesis
Department of Engineering, Enertron Inc., Hohenwald, Tennessee, USA
- 1 Department of Engineering, Enertron Inc., Hohenwald, Tennessee, USA
Advances in Pure Mathematics·Volume 15 (2025)·Pages 36–72·Published 14 January 2025·DOI10.4236/apm.2025.151002
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Abstract
This paper attempts to form a bridge between a sum of the divisors function and the gamma function, proposing a novel approach that could have significant implications for classical problems in number theory, specifically the Robin inequality and the Riemann hypothesis. The exploration of using invariant properties of these functions to derive insights into twin primes and sequential primes is a potentially innovative concept that deserves careful consideration by the mathematical community.
KeywordsLambertW FunctionPrincipal BranchRiemann HypothesisIterationsRobin InequalityRobin IntegersInvarianceGauss Gamma FunctionLi-FunctionPrime Counting FunctionSums of DivisorsInvariancePrimesTwin Primes
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