The Weighted Euler-Maclaurin Formula for a simple integral polytope
  We give an Euler-Maclaurin formula with remainder for the weighted sum of the values of a smooth function on the integral points in a simple integral polytope. Our work generalizes the formula obtained by Karshon, Sternberg and Weitsman in the ''Euler-Maclaurin with remainder for a simple integral polytope''. 
Jose Agapito and Jonathan Weitsman