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Addition of Sequences: Study of Representation Functions by Probability Methods

In: Sequences

Author

Listed:
  • H. Halberstam

    (University of Illinois, Department of Mathematics)

  • K. F. Roth

    (Imperial College of Science and Technology, Department of Mathematics)

Abstract

One often has occasion to ask whether or not there exists an integer sequence possessing certain (e.g. additive) properties; many of the questions considered in other chapters are also of this type. Obviously, the most direct way of obtaining an affirmative answer to such a question is actually to construct a sequence with the required properties. But even when this direct approach proves impracticable, it may still be possible to establish the existence of such a sequence by showing that, in some sense, integer sequences possess the required properties ‘on average’. Indeed, in most branches of mathematics, one often finds that it is much easier to prove that an event occurs ‘on average’ than to give a specific example of such an event.

Suggested Citation

  • H. Halberstam & K. F. Roth, 1983. "Addition of Sequences: Study of Representation Functions by Probability Methods," Springer Books, in: H. Halberstam & K. F. Roth (ed.), Sequences, chapter 0, pages 107-185, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-8227-0_3
    DOI: 10.1007/978-1-4613-8227-0_3
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