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Chebyshevskii Sb., 2018, Volume 19, Issue 2, Pages 529–532 (Mi cheb671)  

On a version of Mertens's theorem

A. Ghiyasi

Allameh Tabataba'i University, School of Mathematical Sciences and Computer, the Department of Mathematics; Iran, Tehran

Abstract: The theorem on the convergence of a product absolutely and conditionally convergent series, which is defined through the discrete integral in the N.V. Bugaev's sense, was proved. Number-theoretical examples, which illustrate this theorem, are given.

Keywords: absolutely and conditionally convergent series, the Mertens's theorem on a product of series, Bernoulli's polynomials, Riemann's zeta-function.

DOI: https://doi.org/10.22405/2226-8383-2018-19-2-529-532

Full text: PDF file (263 kB)
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UDC: 511
Received: 06.07.2018
Accepted:17.08.2018

Citation: A. Ghiyasi, “On a version of Mertens's theorem”, Chebyshevskii Sb., 19:2 (2018), 529–532

Citation in format AMSBIB
\Bibitem{Ghi18}
\by A.~Ghiyasi
\paper On a version of Mertens's theorem
\jour Chebyshevskii Sb.
\yr 2018
\vol 19
\issue 2
\pages 529--532
\mathnet{http://mi.mathnet.ru/cheb671}
\crossref{https://doi.org/10.22405/2226-8383-2018-19-2-529-532}
\elib{http://elibrary.ru/item.asp?id=37112171}


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