On a version of Mertens's theorem
Čebyševskij sbornik, Tome 19 (2018) no. 2, pp. 529-532
Cet article a éte moissonné depuis la source Math-Net.Ru
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, Riemann's zeta-function.
Mots-clés : Bernoulli's polynomials
Mots-clés : Bernoulli's polynomials
@article{CHEB_2018_19_2_a36,
author = {A. Ghiyasi},
title = {On a version of {Mertens's} theorem},
journal = {\v{C}eby\v{s}evskij sbornik},
pages = {529--532},
year = {2018},
volume = {19},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/CHEB_2018_19_2_a36/}
}
A. Ghiyasi. On a version of Mertens's theorem. Čebyševskij sbornik, Tome 19 (2018) no. 2, pp. 529-532. http://geodesic.mathdoc.fr/item/CHEB_2018_19_2_a36/
[1] H. Davenport, “On some infinite series invjlving arithmetical functions”, J. London Math. Soc., 11 (1936), 8–14 | MR
[2] G. I. Arhipov, V. A. Sadovnichij, V. N. CHubarikov, Lekcii po matematicheskomu analizu, Izd. 6-oe, Drofa, M., 1987
[3] G. I. Arkhipov, V. N. Chubarikov, A. A. Karatsuba, Trigonometric Sums in Number Theory and Analysis, de Gruyter Expositions in Mathematics, 39, Walter de Gruyter, Berlin–New York, 2004 | MR | Zbl