Abstract: Let be the von Mangoldt function and be the counting function for the Goldbach numbers. Let and assume that the Riemann Hypothesis holds. We prove that
where runs over the non-trivial zeros of the Riemann zeta-function . This improves a recent result by Bhowmik and Schlage-Puchta.
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Alessandro Languasco Affiliation:
Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Trieste 63, 35121 Padova, Italy
Email:
languasco@math.unipd.it
Alessandro Zaccagnini Affiliation:
Dipartimento di Matematica, Università di Parma, Parco Area delle Scienze 53/a, Campus Universitario, 43124 Parma, Italy
Email:
alessandro.zaccagnini@unipr.it