Improved bounds for arithmetic progressions in product sets
2015 ◽
Vol 11
(08)
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pp. 2295-2303
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Keyword(s):
Let B be a set of natural numbers of size n. We prove that the length of the longest arithmetic progression contained in the product set B.B = {bb′|b, b′ ∈ B} cannot be greater than O(n log n) which matches the lower bound provided in an earlier paper up to a multiplicative constant. For sets of complex numbers, we improve the bound to Oϵ(n1 + ϵ) for arbitrary ϵ > 0 assuming the GRH.
2008 ◽
Vol 78
(3)
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pp. 431-436
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2003 ◽
Vol 12
(5-6)
◽
pp. 599-620
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Keyword(s):
2011 ◽
Vol 07
(04)
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pp. 921-931
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Keyword(s):
2015 ◽
Vol 11
(03)
◽
pp. 801-833
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Keyword(s):
2009 ◽
Vol 05
(04)
◽
pp. 625-634