Enlarged major arcs in additive problems. II
Informatics and Automation, Number theory, algebra, and analysis, Tome 276 (2012), pp. 182-197
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Enlarged major arcs of the circle method are treated, and as consequences new bounds for the exceptional sets in the Waring–Goldbach problem for fourth and fifth powers are obtained.
@article{TRSPY_2012_276_a14,
     author = {Jianya Liu},
     title = {Enlarged major arcs in additive {problems.~II}},
     journal = {Informatics and Automation},
     pages = {182--197},
     year = {2012},
     volume = {276},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2012_276_a14/}
}
TY  - JOUR
AU  - Jianya Liu
TI  - Enlarged major arcs in additive problems. II
JO  - Informatics and Automation
PY  - 2012
SP  - 182
EP  - 197
VL  - 276
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2012_276_a14/
LA  - en
ID  - TRSPY_2012_276_a14
ER  - 
%0 Journal Article
%A Jianya Liu
%T Enlarged major arcs in additive problems. II
%J Informatics and Automation
%D 2012
%P 182-197
%V 276
%U http://geodesic.mathdoc.fr/item/TRSPY_2012_276_a14/
%G en
%F TRSPY_2012_276_a14
Jianya Liu. Enlarged major arcs in additive problems. II. Informatics and Automation, Number theory, algebra, and analysis, Tome 276 (2012), pp. 182-197. http://geodesic.mathdoc.fr/item/TRSPY_2012_276_a14/

[1] Choi K.-K.S., Liu J., “Small prime solutions of quadratic equations”, Can. J. Math., 54 (2002), 71–91 | DOI | MR | Zbl

[2] Gallagher P.X., “A large sieve density estimate near $\sigma =1$”, Invent. math., 11 (1970), 329–339 | DOI | MR | Zbl

[3] Karatsuba A.A., Basic analytic number theory, Springer, Berlin, 1993 | MR | Zbl

[4] Kawada K., Wooley T.D., “On the Waring–Goldbach problem for fourth and fifth powers”, Proc. London Math. Soc. Ser. 3., 83 (2001), 1–50 | DOI | MR | Zbl

[5] Kumchev A.V., “On the Waring–Goldbach problem: exceptional sets for sums of cubes and higher powers”, Can. J. Math., 57 (2005), 298–327 | DOI | MR | Zbl

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

[7] Liu J., Ye J., “Mean-value estimates for nonlinear Weyl sums over primes”, Japan. J. Math. New Ser., 31 (2005), 379–390 | MR | Zbl

[8] Liu J., “Enlarged major arcs in additive problems”, Math. Notes, 88 (2010), 395–401 | DOI | DOI | MR | Zbl

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

[10] Saffari B., Vaughan R.C., “On the fractional parts of $x/n$ and related sequences. II”, Ann. Inst. Fourier., 27:2 (1977), 1–30 | DOI | MR | Zbl

[11] Thanigasalam K., “On sums of positive integral powers and simple proof of $G(6)\leq 31$”, Bull. Calcutta Math. Soc., 81 (1989), 279–294 | MR | Zbl