The Density ofBh[g] Sequences and the Minimum of Dense Cosine Sums
✍ Scribed by Mihail N. Kolountzakis
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 279 KB
- Volume
- 56
- Category
- Article
- ISSN
- 0022-314X
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✦ Synopsis
A set E of integers is called a B h [ g] set if every integer can be written in at most g different ways as a sum of h elements of E. We give an upper bound for the size of a B h [1] subset [n 1 , ..., n k ] of [1, ..., n] whenever h=2m is an even integer:
For the case h=2 (h=4) this has already been proved by Erdo s and Tura n (by Lindstro m). It has been independently proved for all even h by Jia [9] who used an elementary combinatorial argument. Our method uses a result, which we prove, related to the minimum of dense cosine sums which roughly states that if
Finally we exhibit some dense finite and infinite B 2 [2] sequences.
1996 Academic Press, Inc. a B h [ g] set if r E (x; h) g for all x. A B h [1] set is also called a B h set and B 2 sets are sometimes called Sidon sets (the term ``Sidon set'' appears with a different meaning in harmonic analysis). The letter C stands for an arbitrary positive constant in this paper.