Irreducible solutions of an equation involving reciprocals
Sbornik. Mathematics, Tome 208 (2017) no. 12, pp. 1818-1834 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An asymptotic formula, with a new estimate for the remainder term, is obtained for the number of solutions of a symmetric Diophantine equation involving reciprocal integers. Bibliography: 7 titles.
Keywords: reciprocals, moments of Kloosterman sums.
Mots-clés : Diophantine equations
@article{SM_2017_208_12_a4,
     author = {S. V. Konyagin and M. A. Korolev},
     title = {Irreducible solutions of an equation involving reciprocals},
     journal = {Sbornik. Mathematics},
     pages = {1818--1834},
     year = {2017},
     volume = {208},
     number = {12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2017_208_12_a4/}
}
TY  - JOUR
AU  - S. V. Konyagin
AU  - M. A. Korolev
TI  - Irreducible solutions of an equation involving reciprocals
JO  - Sbornik. Mathematics
PY  - 2017
SP  - 1818
EP  - 1834
VL  - 208
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/SM_2017_208_12_a4/
LA  - en
ID  - SM_2017_208_12_a4
ER  - 
%0 Journal Article
%A S. V. Konyagin
%A M. A. Korolev
%T Irreducible solutions of an equation involving reciprocals
%J Sbornik. Mathematics
%D 2017
%P 1818-1834
%V 208
%N 12
%U http://geodesic.mathdoc.fr/item/SM_2017_208_12_a4/
%G en
%F SM_2017_208_12_a4
S. V. Konyagin; M. A. Korolev. Irreducible solutions of an equation involving reciprocals. Sbornik. Mathematics, Tome 208 (2017) no. 12, pp. 1818-1834. http://geodesic.mathdoc.fr/item/SM_2017_208_12_a4/

[1] S. V. Konyagin, M. A. Korolev, “On a symmetric diophantine equation with reciprocals”, Proc. Steklov Inst. Math., 294 (2016), 67–77 | DOI | DOI | MR | Zbl

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

[3] D. A. Mit'kin, “Estimates of certain arithmetic sums related to the number of divisors”, Math. Notes, 80:3 (2006), 449–450 | DOI | DOI | MR | Zbl

[4] A. A. Karatsuba, “Analogues of Kloosterman sums”, Izv. Math., 59:5 (1995), 971–981 | DOI | MR | Zbl

[5] A. A. Karatsuba, “Fractional parts of functions of a special form”, Izv. Math., 59:4 (1995), 721–740 | DOI | MR | Zbl

[6] J. Rosser, L. Schoenfeld, “Approximate formulas for some functions of prime numbers”, Illinois J. Math., 6:1 (1962), 64–94 | MR | Zbl

[7] Yu. N. Shteinikov, “On the product sets of rational numbers”, Proc. Steklov Inst. Math., 296 (2017), 243–250 | DOI | DOI | MR | Zbl