Geodesic
On the product sets of rational numbers
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and combinatorial number theory, Tome 296 (2017), pp. 252-259.

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

A new lower bound on the size of product sets of rational numbers is obtained. An upper estimate for the multiplicative energy of two sets of rational numbers is also found. 
@article{TM_2017_296_a18,
     author = {Yu. N. Shteinikov},
     title = {On the product sets of rational numbers},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {252--259},
     publisher = {mathdoc},
     volume = {296},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2017_296_a18/}
}
TY  - JOUR
AU  - Yu. N. Shteinikov
TI  - On the product sets of rational numbers
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2017
SP  - 252
EP  - 259
VL  - 296
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2017_296_a18/
LA  - ru
ID  - TM_2017_296_a18
ER  - 
%0 Journal Article
%A Yu. N. Shteinikov
%T On the product sets of rational numbers
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2017
%P 252-259
%V 296
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2017_296_a18/
%G ru
%F TM_2017_296_a18
Yu. N. Shteinikov. On the product sets of rational numbers. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and combinatorial number theory, Tome 296 (2017), pp. 252-259. http://geodesic.mathdoc.fr/item/TM_2017_296_a18/

[1] Bourgain J., Konyagin S. V., Shparlinski I. E., “Product sets of rationals, multiplicative translates of subgroups in residue rings, and fixed points of the discrete logarithm”, Int. Math. Res. Not., 2008 (2008), Pap. rnn090 | MR

[2] Cilleruelo J., “On product sets of rationals”, Int. J. Number Theory, 12:5 (2016), 1415–1420 | DOI | MR | Zbl

[3] Cilleruelo J., Garaev M. Z., “Congruences involving product of intervals and sets with small multiplicative doubling modulo a prime and applications”, Math. Proc. Cambridge Philos. Soc., 160:3 (2016), 477–494 | DOI | MR

[4] Cilleruelo J., Ramana D. S., Ramaré O., “The number of rational numbers determined by large sets of integers”, Bull. London Math. Soc., 42:3 (2010), 517–526 | DOI | MR | Zbl

[5] Silleruelo Kh., Ramana D. S., Ramare O., “Chastnye i proizvedeniya podmnozhestv nulevoi plotnosti mnozhestva naturalnykh chisel”, Tr. MIAN, 296, 2017, 58–71

[6] Konyagin S. V., Shkredov I. D., “Novye rezultaty o summakh i proizvedeniyakh v $\mathbb R$”, Tr. MIAN, 294, 2016, 87–98 | DOI | Zbl

[7] Prachar K., Primzahlverteilung, Springer, Berlin, 1957 | MR | Zbl

[8] Schnirelmann L., “Über additive Eigenschaften von Zahlen”, Math. Ann., 107 (1933), 649–690 | DOI | MR | Zbl

[9] Shteinikov Yu. N., “Otsenki trigonometricheskikh summ po podgruppam i nekotorye ikh prilozheniya”, Mat. zametki, 98:4 (2015), 606–625 | DOI | MR | Zbl

[10] Shteinikov Yu. N., “Dopolnenie k rabote Kh. Silleruelo, D. S. Ramany, O. Ramare ‘Chastnye i proizvedeniya podmnozhestv nulevoi plotnosti mnozhestva naturalnykh chisel’ ”, Tr. MIAN, 296, 2017, 260–264

[11] Tao T., Vu V. H., Additive combinatorics, Cambridge Univ. Press, Cambridge, 2006 | MR | Zbl