Geodesic
The distribution of Hardy–Littlewood numbers in arithmetic progressions
Izvestiya. Mathematics, Tome 34 (1990) no. 1, pp. 213-228 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An asymptotic formula is obtained for the number of solutions of the congruence $$ p+n^2\equiv l\ (\operatorname{mod}D),\qquad p\leqslant x,\quad n\leqslant\sqrt x,\quad(l,D)=1, $$ where $D$ is a sufficiently large prime. Bibliography: 7 titles. 
@article{IM2_1990_34_1_a9,
     author = {Z. Kh. Rakhmonov},
     title = {The distribution of {Hardy{\textendash}Littlewood} numbers in arithmetic progressions},
     journal = {Izvestiya. Mathematics},
     pages = {213--228},
     year = {1990},
     volume = {34},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1990_34_1_a9/}
}
TY  - JOUR
AU  - Z. Kh. Rakhmonov
TI  - The distribution of Hardy–Littlewood numbers in arithmetic progressions
JO  - Izvestiya. Mathematics
PY  - 1990
SP  - 213
EP  - 228
VL  - 34
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IM2_1990_34_1_a9/
LA  - en
ID  - IM2_1990_34_1_a9
ER  - 
%0 Journal Article
%A Z. Kh. Rakhmonov
%T The distribution of Hardy–Littlewood numbers in arithmetic progressions
%J Izvestiya. Mathematics
%D 1990
%P 213-228
%V 34
%N 1
%U http://geodesic.mathdoc.fr/item/IM2_1990_34_1_a9/
%G en
%F IM2_1990_34_1_a9
Z. Kh. Rakhmonov. The distribution of Hardy–Littlewood numbers in arithmetic progressions. Izvestiya. Mathematics, Tome 34 (1990) no. 1, pp. 213-228. http://geodesic.mathdoc.fr/item/IM2_1990_34_1_a9/

[1] Karatsuba A. A., “Raspredelenie proizvedenii sdvinutykh prostykh chisel v arifmeticheskikh progressiyakh”, Dokl. AN SSSR, 192:4 (1970), 724–727 | Zbl

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

[3] Babaev G. B., “Zamechanie k rabote Devenporta i Kheilbrona”, UMN, 13:6(84) (1958), 63–64 | MR | Zbl

[4] Petechuk M. M., “Summa znachenii funktsii delitelei v arifmeticheskikh progressiyakh s raznostyu, ravnoi stepeni nechetnogo prostogo chisla”, Izv. AN SSSR. Ser. matem., 43:4 (1979), 892–908 | MR | Zbl

[5] Hardy G. H., Wright E. M., An introduction to the theory of numbers, Oxford at the clarendon press, 1954 | MR | Zbl

[6] Friendlander T. B., Iwaniec H., “The divisor problem for arithmetic progression”, Acta Arithmetica, XLV:3 (1985), 273–277 | MR

[7] Weil A., “On some exponential sams”, Proc. Nat. Acad. SUSA, 34:5 (1948), 204–207 | DOI | MR | Zbl