Perfect difference sets constructed from Sidon sets

14 páginas.-- Mathematics Subject Classification (2000): 11B13; 11B34.A set A of positive integers is a perfect difference set if every nonzero integer has a unique representation as the difference of two elements of A. We construct dense perfect difference sets from dense Sidon sets. As a consequence of this new approach we prove that there exists a perfect difference set A such that A(x) x √2−1−o(1). Also we prove that there exists a perfect difference set A such that limsup x→∞ A(x)/√x≥ 1/√2.The work of J. C. was supported by Grant MTM 2005-04730 of MYCIT (Spain). The work of M. B. N. was supported in part by grants from the NSA Mathematical Sciences Program and the PSC-CUNY Research Award Program.Peer reviewe