About Riemann's Zeta-Function and Applications

Authors

  • N. Daili Department of Mathematics, Faculty of Sciences, University, Setif 1, El Bez. 19000 Setif,

DOI:

https://doi.org/10.26713/cma.v11i3.1399

Keywords:

Theoretic arithmetic function, Riemann zeta-function, Functional equation, Applications

Abstract

In this paper we give some remarks on the Riemann's zeta-function related to theoretic arithmetic functions and some applications.

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References

P. Borwein, S. Choi, B. Rooney and A. Weirathmueller, The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike, Springer-Verlag (2007), URL: https://pdfs.semanticscholar.org/d498/a6c9fda1bef6a3e4feec2034e33fd864826f.pdf.

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N. Daili, About Dirichlet's Transformation and Theoretic-Arithmetic Functions, General Mathematics Notes 3(2) (2011), 108 – 112, URL: https://www.researchgate.net/profile/N_Daili/publication/326658457.

G.-J. De La Vallée Poussin, Recherches analytiques sur la théorie des nombres premiers, Ann. Soc. Scient. Bruxelles 20 (1896), 183 – 256.

L. Euler, Variae observationes circa series infinitas (Various Observations about Infinite Series), Thesis, published by St. Petersburg Academy in 1737, URL: https://publicacions.iec.cat/Front/repository/pdf/00000123/00000101.pdf.

H. M. Edwards, Riemann's Zeta Function, Dover Publications, New York (1974), URL: https://books.google.co.in/books?id=ruVmGFPwNhQC&printsec=frontcover#v=onepage&q&f=false.

J. Hadamard, Sur la distribution des zéros de la fonction Zeta et ses conséquences arithmétiques, Bulletin de la Société Mathématique de France 24 (1896), 199 – 220, DOI: 10.24033/bsmf.545.

B. Riemann, On the Number of Prime Numbers less than a Given Quantity, Translated by D. R. Wilkins, Clay Mathematics Institute (1998), URL: https://www.claymath.org/sites/default/files/ezeta.pdf.

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Published

30-09-2020
CITATION

How to Cite

Daili, N. (2020). About Riemann’s Zeta-Function and Applications. Communications in Mathematics and Applications, 11(3), 461–479. https://doi.org/10.26713/cma.v11i3.1399

Issue

Vol. 11 No. 3 (2020)

Section

Research Article

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