Geodesic
On a~symmetric diophantine equation with reciprocals
Informatics and Automation, Modern problems of mathematics, mechanics, and mathematical physics. II, Tome 294 (2016), pp. 76-86.

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

An asymptotic formula is obtained for the number of solutions to a symmetric Diophantine equation with reciprocals, and its applications to problems related to the distribution of values of short Kloosterman sums are presented. 
@article{TRSPY_2016_294_a3,
     author = {S. V. Konyagin and M. A. Korolev},
     title = {On a~symmetric diophantine equation with reciprocals},
     journal = {Informatics and Automation},
     pages = {76--86},
     publisher = {mathdoc},
     volume = {294},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2016_294_a3/}
}
TY  - JOUR
AU  - S. V. Konyagin
AU  - M. A. Korolev
TI  - On a~symmetric diophantine equation with reciprocals
JO  - Informatics and Automation
PY  - 2016
SP  - 76
EP  - 86
VL  - 294
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2016_294_a3/
LA  - ru
ID  - TRSPY_2016_294_a3
ER  - 
%0 Journal Article
%A S. V. Konyagin
%A M. A. Korolev
%T On a~symmetric diophantine equation with reciprocals
%J Informatics and Automation
%D 2016
%P 76-86
%V 294
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2016_294_a3/
%G ru
%F TRSPY_2016_294_a3
S. V. Konyagin; M. A. Korolev. On a~symmetric diophantine equation with reciprocals. Informatics and Automation, Modern problems of mathematics, mechanics, and mathematical physics. II, Tome 294 (2016), pp. 76-86. http://geodesic.mathdoc.fr/item/TRSPY_2016_294_a3/

[1] Karatsuba A. A., “Analogi summ Kloostermana”, Izv. RAN. Ser. mat., 59:5 (1995), 93–102 | MR | Zbl

[2] Snurnitsyn P. V., “Ob otsenke srednego znacheniya korotkoi summy Kloostermana”, Uchen. zap. Orlov. gos. un-ta. Estestv., tekhnich. i medits. nauki, 2012, no. 6-2, 212–215

[3] Burgein Zh., Garaev M. Z., “Summa mnozhestv, obrazovannykh obratnymi elementami v polyakh prostogo poryadka, i polilineinye summy Kloostermana”, Izv. RAN. Ser. mat., 78:4 (2014), 19–72 | DOI | MR | Zbl

[4] Heath-Brown D. R., The density of rational points on Cayley's cubic surface, Proceedings of the session in analytic number theory and Diophantine equations (Bonn, 2002), Bonner Math. Schriften, 360, Univ. Bonn, Bonn, 2003, 33 pp. | MR | Zbl

[5] Mardzhanishvili K. K., “Otsenka odnoi arifmeticheskoi summy”, DAN SSSR, 22:7 (1939), 391–393

[6] Timergaliev I. S., “O raspredelenii znachenii analogov summ Kloostermana”, Vestn. Mosk. un-ta. Matematika. Mekhanika, 2013, no. 5, 37–41 | MR | Zbl

[7] Boyarinov R. N., Veroyatnostnye metody v teorii chisel i prilozheniya v teorii argumenta dzeta-funktsii Rimana, Dis. $\dots$ dokt. fiz.-mat. nauk, MGU, M., 2012

[8] Boyarinov R. N., “O skorosti skhodimosti raspredelenii sluchainykh velichin”, DAN, 435:3 (2010), 295–297 | MR | Zbl