The Density of B H G] Sequences and the Minimum of Dense Cosine Sums
نویسنده
چکیده
A set E of integers is called a B h g] set if every integer can be written in at most g diierent ways as a sum of h elements of E. We give an upper bound for the size of a B h 1] subset fn 1 ; : : :; n k g of f1; : : :; ng whenever h = 2m is an even integer: k ? m(m!) 2 1=h n 1=h + O(n 1=2h): For the case h = 2 (h = 4) this has already been proved by Erd} os and Turr an (by Lindstrr om). 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 1 1 < < N (2 ?)N are N diierent integers then min x N X 1 cos j x C 2 N: Finally we exhibit some dense nite and innnite B 2 2] sequences.
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تاریخ انتشار 1996