Geodesic
Some New Results on Sums of Primes
Matematičeskie zametki, Tome 90 (2011) no. 1, pp. 11-21.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study sums of primes by means of a generalization of Euler's prime number theorem and use the values of the Riemann zeta function for the approximation. We also give the truncation error of these approximations.
Keywords: number theory, prime sums, elliptic theta functions, Möbius function, Möbius inversion theorem, Riemann zeta function, Euler's prime number theorem.
Mots-clés : Euler-totient constant 
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N. Bagis. Some New Results on Sums of Primes. Matematičeskie zametki, Tome 90 (2011) no. 1, pp. 11-21. http://geodesic.mathdoc.fr/item/MZM_2011_90_1_a1/

[1] T. M. Apostol, Introduction to Analytic Number Theory, Undergrad. Texts in Math., Springer-Verlag, New York, 1976 | MR | Zbl

[2] B. C. Berndt, Ramanujan's Notebooks, Part III, Springer Verlang, New York, 1991 | MR | Zbl

[3] T. W. Körner, Fourier Analysis, Cambridge Univ. Press, Cambridge, 1988 | MR | Zbl

[4] G. E. Andrews, Number Theory, Dover Publ., New York, 1994 | MR | Zbl

[5] B. C. Berndt, Ramanujan's Notebooks, Part I, Springer-Verlag, New York, 1985 | MR | Zbl