Geodesic
Difference sets are not multiplicatively closed
Discrete analysis (2016) Cet article a éte moissonné depuis la source Scholastica

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We prove that for any finite set A of real numbers its difference set D:=A-A has large product set and quotient set, namely, |DD|, |D/D| \gg |D|^{1+c}, where c>0 is an absolute constant. A similar result takes place in the prime field F_p for sufficiently small D. It gives, in particular, that multiplicative subgroups of size less than p^{4/5-\eps} cannot be represented in the form A-A for any A from F_p.
Publié le : 
@article{DAS_2016_a2,
     author = {Ilya D. Shkredov},
     title = {Difference sets are not multiplicatively closed},
     journal = {Discrete analysis},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2016_a2/}
}
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AU  - Ilya D. Shkredov
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JO  - Discrete analysis
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LA  - en
ID  - DAS_2016_a2
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%A Ilya D. Shkredov
%T Difference sets are not multiplicatively closed
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%U http://geodesic.mathdoc.fr/item/DAS_2016_a2/
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Ilya D. Shkredov. Difference sets are not multiplicatively closed. Discrete analysis (2016). http://geodesic.mathdoc.fr/item/DAS_2016_a2/