A NOTE ON A RESULT OF RUZSA, II

作者：Tang, Min^*

来源：Bulletin of the Australian Mathematical Society, 2010, 82(2): 340-347.

DOI：10.1017/S0004972710000353

• Erdos-Turan conjecture
• basis

Let sigma(A)(n)= vertical bar{(a, a') is an element of A(2) : a + a' = n}vertical bar, where n is an element of N and A is a subset of N. Erdos and Turan conjectured that for any basis A of N, sigma(A)(n) is unbounded. In 1990, Ruzsa constructed a basis A subset of N for which sigma(A)(n) is bounded in square mean. Based on Ruzsa's method, we proved that there exists a basis A of N satisfying Sigma(n <= N) sigma(2)(A)(n) <= 1 449 757 928N for large enough N. In this paper, we give a quantitative result for the existence of N. that is, we show that there exists a basis A of N satisfying Sigma(n <= N) sigma(2)(A) (n) <= 1 069 693 154N for N >= 7.628 517 798 x 10(27), which improves earlier results of the author ['A note on a result of Ruzsa', Bull. Aust. Math. Soc. 77 (2008), 91-98].

• 出版日期2010-10
• 单位安徽师范大学