On the product sets of rational numbers
Informatics and Automation, Analytic and combinatorial number theory, Tome 296 (2017), pp. 252-259.

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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.
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Yu. N. Shteinikov. On the product sets of rational numbers. Informatics and Automation, Analytic and combinatorial number theory, Tome 296 (2017), pp. 252-259. http://geodesic.mathdoc.fr/item/TRSPY_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