Smith Minkowski Siegel Mass Formula
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Smith Minkowski Siegel mass formula (or Minkowski Siegel mass formula) is a formula for the sum of the weights of the lattices (quadratic forms) in a genus, weighted by the reciprocals of the orders of their automorphism groups. The mass formula is often given for integral quadratic forms, though it can be generalized to quadratic forms over any algebraic number field. In 0 and 1 dimensions the mass formula is trivial, in 2 dimensions it is essenti...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Smith Minkowski Siegel mass formula (or Minkowski Siegel mass formula) is a formula for the sum of the weights of the lattices (quadratic forms) in a genus, weighted by the reciprocals of the orders of their automorphism groups. The mass formula is often given for integral quadratic forms, though it can be generalized to quadratic forms over any algebraic number field. In 0 and 1 dimensions the mass formula is trivial, in 2 dimensions it is essentially equivalent to Dirichlet''s class number formulas for imaginary quadratic fields, and in 3 dimensions some partial results were given by Ferdinand Eisenstein. The mass formula in higher dimensions was first given by H. J. S. Smith (1867), though his results were forgotten for many years. It was rediscovered by H. Minkowski (1885), and an error in Minkowski''s paper was found and corrected by C. L. Siegel (1935).
