An explicit version of Shimura's reciprocity law for Siegel modular   functions
  We give an explicit version of Shimura's reciprocity law for singular values of Siegel modular functions. We use this to construct the first examples of class invariants of quartic CM fields that are smaller than Igusa invariants. Our statement also enables a new proof of Shimura's reciprocity law by Tonghai Yang. 
Marco Streng
math.NT