Geodesic
Quotient and product sets of thin subsets of the positive integers
Informatics and Automation, Analytic and combinatorial number theory, Tome 296 (2017), pp. 58-71.

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

We study the cardinalities of $A/A$ and $AA$ for thin subsets $A$ of the set of the first $n$ positive integers. In particular, we consider the typical size of these quantities for random sets $A$ of zero density and compare them with the sizes of $A/A$ and $AA$ for subsets of the shifted primes and the set of sums of two integral squares. 
@article{TRSPY_2017_296_a4,
     author = {J. Cilleruelo and D. S. Ramana and O. Ramar\'e},
     title = {Quotient and product sets of thin subsets of the positive integers},
     journal = {Informatics and Automation},
     pages = {58--71},
     publisher = {mathdoc},
     volume = {296},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2017_296_a4/}
}
TY  - JOUR
AU  - J. Cilleruelo
AU  - D. S. Ramana
AU  - O. Ramaré
TI  - Quotient and product sets of thin subsets of the positive integers
JO  - Informatics and Automation
PY  - 2017
SP  - 58
EP  - 71
VL  - 296
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2017_296_a4/
LA  - ru
ID  - TRSPY_2017_296_a4
ER  - 
%0 Journal Article
%A J. Cilleruelo
%A D. S. Ramana
%A O. Ramaré
%T Quotient and product sets of thin subsets of the positive integers
%J Informatics and Automation
%D 2017
%P 58-71
%V 296
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2017_296_a4/
%G ru
%F TRSPY_2017_296_a4
J. Cilleruelo; D. S. Ramana; O. Ramaré. Quotient and product sets of thin subsets of the positive integers. Informatics and Automation, Analytic and combinatorial number theory, Tome 296 (2017), pp. 58-71. http://geodesic.mathdoc.fr/item/TRSPY_2017_296_a4/

[1] Cilleruelo J., Guijarro-Ordóñez J., “Ratio sets of random sets”, Ramanujan J., 2015 | DOI

[2] Cilleruelo J., Lê T. H., “On a question of Sárközy on gaps of product sequences”, Isr. J. Math., 179 (2010), 285–295 | DOI | MR | Zbl

[3] 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

[4] Elekes G., Ruzsa I. Z., “Few sums, many products”, Stud. sci. math. Hung., 40:3 (2003), 301–308 | MR | Zbl

[5] Erdësh P., “Ob odnom asimptoticheskom neravenstve v teorii chisel”, Vestn. Leningr. un-ta. Matematika, mekhanika, astronomiya, 15:13(3) (1960), 41–49 | MR

[6] Ford K., “The distribution of integers with a divisor in a given interval”, Ann. Math. Ser. 2, 168:2 (2008), 367–433 | DOI | MR | Zbl

[7] Halberstam H., Richert H.-E., Sieve methods, Dover Publ., Mineola, NY, 2011 | MR

[8] Mangerel A., The multiplication problem and its generalisations, M. Sc. Thesis, Univ. Toronto, 2014

[9] Nowak W. G., “On the distribution of $M$-tuples of $B$-numbers”, Publ. Inst. Math., 77:91 (2005), 71–78 | DOI | MR | Zbl

[10] Roman S., “The formula of Faà di Bruno”, Amer. Math. Mon., 87:10 (1980), 805–809 | DOI | MR | Zbl

[11] Pomerance C., Sárközy A., “On products of sequences of integers”, Number theory, Proc. Conf. (Budapest, 1987), v. 1, Colloq. Math. Soc. János Bolyai, 51, North-Holland, Amsterdam, 1990, 447–463 | MR

[12] 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