DENSE SETS OF INTEGERS WITH A PRESCRIBED REPRESENTATION FUNCTION
2011 ◽
Vol 84
(1)
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pp. 40-43
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AbstractA set A⊆ℤ is called an asymptotic basis of ℤ if all but finitely many integers can be represented as a sum of two elements of A. Let A be an asymptotic basis of integers with prescribed representation function, then how dense A can be? In this paper, we prove that there exist a real number c>0 and an asymptotic basis A with prescribed representation function such that $A(-x,x)\geq c\sqrt {x}$ for infinitely many positive integers x.
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2017 ◽
Vol 13
(09)
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pp. 2253-2264
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2011 ◽
Vol 48
(1)
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pp. 93-103
2015 ◽
Vol 11
(06)
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pp. 1905-1912
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2004 ◽
Vol 2004
(30)
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pp. 1589-1597
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1984 ◽
Vol 34
(3)
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pp. 355-361
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1953 ◽
Vol 5
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pp. 456-459
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