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Mat. Zametki, 2019, Volume 106, Issue 5, paper published in the English version journal (Mi mz12248)  

Papers published in the English version of the journal

Some Identities Involving the Cesàro Average of the Goldbach Numbers

M. Cantarini

Department of Mathematics and Computer Science, University of Perugia, Perugia, 06123 Italy

Abstract: Let $\Lambda(n)$ be the von Mangoldt function, and let $r_{G}(n):=\sum_{m_{1}+m_{2}=n}\Lambda(m_{1})\Lambda(m_{2})$ be the weighted sum for the number of Goldbach representations which also includes powers of primes. Let $\widetilde{S}(z):=\sum_{n\geq1}\Lambda(n)e^{-nz}$, where $\Lambda(n)$ is the Von Mangoldt function, with $z\in\mathbb{C}, \mathrm{Re}(z)>0$. In this paper, we prove an explicit formula for $\widetilde{S}(z)$ and the Cesàro average of $r_{G}(n)$.

Keywords: Goldbach-type theorems, Laplace transforms, Cesàro average.


English version:
Mathematical Notes, 2019, 106:5, 688–702

Bibliographic databases:

Received: 13.11.2018
Revised: 06.06.2019
Language:

Citation: M. Cantarini, “Some Identities Involving the Cesàro Average of the Goldbach Numbers”, Math. Notes, 106:5 (2019), 688–702

Citation in format AMSBIB
\Bibitem{Can19}
\by M.~Cantarini
\paper Some Identities Involving the Cesàro Average
of the Goldbach Numbers
\jour Math. Notes
\yr 2019
\vol 106
\issue 5
\pages 688--702
\mathnet{http://mi.mathnet.ru/mz12248}
\crossref{https://doi.org/10.1134/S0001434619110038}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85077048720}


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