An explicit formula for the Siegel series of a quadratic form over a   non-archimedian local field
  Let F be a non-archimedian local field of characteristic 0, and O the ring of integres in F. We give an explicit formula for the Siegel series of a half-integral matrix over O. This formula expresses the Siegel series of a half-integral matrix $B$ explicitly in terms of the Gross-Keating invariant of $B$ and its related invariants. 
Tamotsu Ikeda and Hidenori Katsurada
math.NT