• Corpus ID: 14104403

ON A PROBLEM OF SIDON IN ADDITIVE NUMBER THEORY, AND ON SOME RELATED PROBLEMS

@inproceedings{Ebdos2002ONAP,
  title={ON A PROBLEM OF SIDON IN ADDITIVE NUMBER THEORY, AND ON SOME RELATED PROBLEMS},
  author={P Ebdos and Peter Tur},
  year={2002}
}
Let a,<&<... be a sequence of positive integers, and suppose that the suma czi+lzi (where i ,<j) are all different. Such sequences, called B, sequences by Sidont, occur in the theory of Fourier series. Suppose that n is given, and that oz < n < aX+r ; the question was raised by Sidon how large 2 can be ; that is, how many terms not exceeding n a J3, sequence can have. Put x = d(n), and denote by Q(n) the maximum of 4(n) for given n. Sidon observed that Q(n)-> en*, where c ia a positive constant… 
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References

SHOWING 1-2 OF 2 REFERENCES
The proof is similar to that wed by P
  • Erdijs in Mitt. Tomsk Univ
  • 1938
If f(a) > o for n > rt,, then hm f(n) = CD. Here we may mention that the corresponding result for g(n), the number of representation8 of n as ai a, can be proved*. The University of Pennsylvania
  • If f(a) > o for n > rt,, then hm f(n) = CD. Here we may mention that the corresponding result for g(n), the number of representation8 of n as ai a, can be proved*. The University of Pennsylvania