TY - JOUR
T1 - Extremal Properties of Product Sets
AU - Ford, Kevin
N1 - Publisher Copyright:
© 2018, Pleiades Publishing, Ltd.
PY - 2018/11/1
Y1 - 2018/11/1
N2 - We find the nearly optimal size of a set A ⊂ [N]:= {1,..,N} so that the product set AA satisfies either (i) |AA| ~ |A| 2 /2 or (ii) |AA| ~ |[N][N]|. This settles problems recently posed in a paper of J. Cilleruelo, D. S. Ramana and O. Ramaré.
AB - We find the nearly optimal size of a set A ⊂ [N]:= {1,..,N} so that the product set AA satisfies either (i) |AA| ~ |A| 2 /2 or (ii) |AA| ~ |[N][N]|. This settles problems recently posed in a paper of J. Cilleruelo, D. S. Ramana and O. Ramaré.
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U2 - 10.1134/S0081543818080175
DO - 10.1134/S0081543818080175
M3 - Article
AN - SCOPUS:85062501079
SN - 0081-5438
VL - 303
SP - 220
EP - 226
JO - Proceedings of the Steklov Institute of Mathematics
JF - Proceedings of the Steklov Institute of Mathematics
IS - 1
ER -