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DENSE SETS OF INTEGERS WITH A PRESCRIBED REPRESENTATION FUNCTION
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 84 / Issue 1 / August 2011
- Published online by Cambridge University Press:
- 16 June 2011, pp. 40-43
- Print publication:
- August 2011
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- Article
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A 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
for infinitely many positive integers x.
for infinitely many positive integers 