Geodesic
Enlarged Major Arcs in Additive Problems
Matematičeskie zametki, Tome 88 (2010) no. 3, pp. 438-445.

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

Enlarged major arcs in the Waring–Goldbach problem are studied by using large sieve estimates for Dirichlet polynomials and estimates for exponential sums over primes.
Keywords: Waring–Goldbach problem, major and minor arcs on the unit interval, Farey dissection, Dirichlet character. 
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J. Liu. Enlarged Major Arcs in Additive Problems. Matematičeskie zametki, Tome 88 (2010) no. 3, pp. 438-445. http://geodesic.mathdoc.fr/item/MZM_2010_88_3_a11/

[1] A. V. Kumchev, “On Weyl sums over primes and almost primes”, Michigan Math. J., 54:2 (2006), 243–268 | DOI | MR | Zbl

[2] I. M. Vinogradov, Osnovy teorii chisel, Nauka, M., 1981 | MR | Zbl

[3] L.-k. Hua, Tui Lei Su Shu Lun [Additive Prime Number Theory], Science press, Peking, 1957 | MR

[4] X. Ren, “On exponential sums over primes and application in Waring–Goldbach problem”, Sci. China Ser. A, 48:6 (2005), 785–797 | DOI | MR | Zbl

[5] J. Liu, “On Lagrange's theorem with prime variables”, Quart. J. Math. Oxford Ser. (2), 54:4 (2003), 453–462 | DOI | MR | Zbl

[6] A. A. Karatsuba, Osnovy analiticheskoi teorii chisel, Nauka, M., 1983 | MR | Zbl