Note on the sumset of squares

Abstract

It is proved that for any non-empty finite subset $Q$ of the square numbers, $|Q+Q|\ge C^{\prime }|Q|(\log |Q|{)}^{1/3+o(1)}$. This result essentially is proved -- with the same tools -- by Mei-Chu Chang. See in J. Funct. Anal. 207 (2004), no 2, 444-460. So the author will withdraw this ArXiv file.

This result essentially is proved -- with the same tools -- by Mei-Chu Chang. See in J. Funct. Anal. 207 (2004), no 2, 444-460. So the author will withdraw this ArXiv file