Email this article Some Identities Involving the Cesàro Average of the Goldbach Numbers
- Authors: Cantarini M.1
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Affiliations:
- Department of Mathematics and Computer Science
- Issue: Vol 106, No 5-6 (2019)
- Pages: 688-702
- Section: Article
- URL: https://ogarev-online.ru/0001-4346/article/view/151846
- DOI: https://doi.org/10.1134/S0001434619110038
- ID: 151846
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Abstract
Let Λ(n) be the von Mangoldt function, and let rG(n):= ∑m1+m2=n Λ (m1)Λ(m2) be the weighted sum for the number of Goldbach representations which also includes powers of primes. Let S̃(z): = ∑n≥1 Λ (n)e-nz, where Λ (n) is the Von Mangoldt function, with z ∈ ℂ, Re (z) > 0. In this paper, we prove an explicit formula for S̃(z) and the Cesàro average of rG(n).
About the authors
M. Cantarini
Department of Mathematics and Computer Science
Author for correspondence.
Email: marco.cantarini@unipg.it
Italy, Perugia, 06123
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