Fourier-Mukai transformations on K3 surfaces with $\rho =1$ and   Atkin-Lehner involutions
  We show that there is a surjection from the Fourier-Mukai transformations on projective K3 surfaces with the Picard number $\rho (X)=1$ to so called to the group of Atkin-Lehner involutions. This was expected in Hosono-Lian-Oguiso-Yau's paper. 
Kotaro Kawatani
math.AG