Erdős-Turan conjecture

Erdős-Turan conjecture asserts there exist no asymptotic basis ( A0 of order 2 such that its representation function


is boundedPlanetmathPlanetmath.

Alternatively, the question can be phrased as whether there exists a power seriesMathworldPlanetmath F with coefficients 0 and 1 such that all coefficients of F2 are greater than 0, but are bounded.

If we replace set of nonnegative integers by the set of all integers, then the question was settled by Nathanson[2] in negative, that is, there exists a set A such that rA,2(n)=1.


  • 1 Heini Halberstam and Klaus Friedrich Roth. Sequences. Springer-Verlag, second edition, 1983. 0498.10001.
  • 2 Melvyn B. Nathanson. Every functionMathworldPlanetmath is the representation function of an additive basis for the integers.
Title Erdős-Turan conjecture
Canonical name ErdHosTuranConjecture
Date of creation 2013-03-22 13:27:11
Last modified on 2013-03-22 13:27:11
Owner bbukh (348)
Last modified by bbukh (348)
Numerical id 8
Author bbukh (348)
Entry type Conjecture
Classification msc 11B13
Classification msc 11B34
Classification msc 11B05
Related topic SidonSet