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).

Some Identities Involving the Cesàro Average of the Goldbach Numbers

Cantarini M.
2019

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).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1534253
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