Geodesic
The Generalized Estermann Ternary Problem for Noninteger Powers with Almost Equal Summands
Matematičeskie zametki, Tome 100 (2016) no. 3, pp. 410-420.

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

An asymptotic formula in the generalized Estermann ternary problem for noninteger powers with almost equal summands dealing with the representation of a sufficiently large natural number as the sum of two primes and the integer part of a noninteger power of a natural number is proved.
Keywords: Estermann problem, almost equal summands, short trigonometric sum with noninteger exponent, density theorem. 
@article{MZM_2016_100_3_a7,
     author = {P. Z. Rakhmonov},
     title = {The {Generalized} {Estermann} {Ternary} {Problem} for {Noninteger} {Powers} with {Almost} {Equal} {Summands}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {410--420},
     publisher = {mathdoc},
     volume = {100},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_3_a7/}
}
TY  - JOUR
AU  - P. Z. Rakhmonov
TI  - The Generalized Estermann Ternary Problem for Noninteger Powers with Almost Equal Summands
JO  - Matematičeskie zametki
PY  - 2016
SP  - 410
EP  - 420
VL  - 100
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2016_100_3_a7/
LA  - ru
ID  - MZM_2016_100_3_a7
ER  - 
%0 Journal Article
%A P. Z. Rakhmonov
%T The Generalized Estermann Ternary Problem for Noninteger Powers with Almost Equal Summands
%J Matematičeskie zametki
%D 2016
%P 410-420
%V 100
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2016_100_3_a7/
%G ru
%F MZM_2016_100_3_a7
P. Z. Rakhmonov. The Generalized Estermann Ternary Problem for Noninteger Powers with Almost Equal Summands. Matematičeskie zametki, Tome 100 (2016) no. 3, pp. 410-420. http://geodesic.mathdoc.fr/item/MZM_2016_100_3_a7/

[1] T. Estermann, “Proof that every large integer is the sum of two primes and square”, Proc. London math. Soc. (2), 42:1 (1937), 501–516 | DOI | MR | Zbl

[2] Z. Kh. Rakhmonov, “Ternarnaya zadacha Estermana s pochti ravnymi slagaemymi”, Matem. zametki, 74:4 (2003), 564–572 | DOI | MR | Zbl

[3] Z. Kh. Rakhmonov, “Kubicheskaya zadacha Estermana s pochti ravnymi slagaemymi”, Matem. zametki, 95:3 (2014), 445–456 | DOI | MR | Zbl

[4] P. Z. Rakhmonov, “Korotkie summy s netseloi stepenyu naturalnogo chisla”, Matem. zametki, 95:5 (2014), 763–774 | DOI | MR | Zbl

[5] P. Z. Rakhmonov, “Korotkie trigonometricheskie summy s netseloi stepenyu naturalnogo chisla”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2012, no. 6, 51–55 | MR

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

[7] S. M. Voronin, A. A. Karatsuba, Dzeta-funktsiya Rimana, Fizmatlit, M., 1994 | MR | Zbl

[8] Z. Kh. Rakhmonov, “Otsenka plotnosti nulei dzeta-funktsii Rimana”, UMN, 49:2 (296) (1994), 161–162 | MR | Zbl

[9] G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, Teoriya kratnykh trigonometricheskikh summ, Nauka, M., 1987 | MR | Zbl

[10] E. T. Uitteker, Dzh. N. Vatson, Kurs sovremennogo analiza. Ch. 1. Osnovnye operatsii analiza, Fizmatgiz, M., 1963 | Zbl