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We show that there is a surjection from the Fourier-Mukai transformations onprojective K3 surfaces with the Picard number $\rho (X)=1$ to so called to thegroup of Atkin-Lehner involutions. This was expected inHosono-Lian-Oguiso-Yau's paper.

Fourier-Mukai transformations on K3 surfaces with $\rho =1$ and Atkin-Lehner involutions