Geodesic
Estermann's Ternary Problem with Almost Equal Summands
Matematičeskie zametki, Tome 74 (2003) no. 4, pp. 564-572 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We prove an asymptotic formula for the number of representations of a sufficiently large positive integer N as the sum of two primes and the square of a natural number when they are almost equal. 
@article{MZM_2003_74_4_a9,
     author = {Z. Kh. Rakhmonov},
     title = {Estermann's {Ternary} {Problem} with {Almost} {Equal} {Summands}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {564--572},
     year = {2003},
     volume = {74},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_4_a9/}
}
TY  - JOUR
AU  - Z. Kh. Rakhmonov
TI  - Estermann's Ternary Problem with Almost Equal Summands
JO  - Matematičeskie zametki
PY  - 2003
SP  - 564
EP  - 572
VL  - 74
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_2003_74_4_a9/
LA  - ru
ID  - MZM_2003_74_4_a9
ER  - 
%0 Journal Article
%A Z. Kh. Rakhmonov
%T Estermann's Ternary Problem with Almost Equal Summands
%J Matematičeskie zametki
%D 2003
%P 564-572
%V 74
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_2003_74_4_a9/
%G ru
%F MZM_2003_74_4_a9
Z. Kh. Rakhmonov. Estermann's Ternary Problem with Almost Equal Summands. Matematičeskie zametki, Tome 74 (2003) no. 4, pp. 564-572. http://geodesic.mathdoc.fr/item/MZM_2003_74_4_a9/

[1] Estermann T., “Proof that every large integer is the sum of two primes and square”, Proc. London Math. Soc., 11 (1937), 501–516 | DOI

[2] Rakhmonov Z. Kh., “Srednie znacheniya funktsii Chebysheva v korotkikh intervalakh”, Sovremennye problemy matematiki i mekhaniki, Tr. mezhdunarodnoi konferentsii, posvyaschennoi 175-letiyu P. L. Chebysheva, MGU, M., 1996, 125–189

[3] Rakhmonov Z. Kh., “Korotkie lineinye trigonometricheskie summy s prostymi chislami”, Dokl. AN RT, 43:3 (2000)

[4] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., Teoriya kratnykh trigonometricheskikh summ, Nauka, M., 1987

[5] Vinogradov I. M., Metod trigonometricheskikh summ v teorii chisel, Nauka, M., 1976

[6] Zhan Tao, “On represention of a large odd integer as a sum of three almost primes”, Acta Math. Sinica, 7:3 (1991), 259–272 | DOI | MR | Zbl