Note on the sumset of squares

It is proved that for any non-empty finite subset $Q$ of the square numbers, $\mathrm{\mid }Q+Q\mathrm{\mid }\ge C^{\mathrm{\prime }}\mathrm{\mid }Q\mathrm{\mid }(\log \mathrm{\mid }Q\mathrm{\mid }{)}^{1\mathrm{/}3+o(1)}$. 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.