Siegel–Weil formula

Short description: Expresses Eisenstein series as a weighted average of theta series of lattices in a genus

In mathematics, the Siegel–Weil formula, introduced by Weil (1964, 1965) as an extension of the results of Siegel (1951, 1952), expresses an Eisenstein series as a weighted average of theta series of lattices in a genus, where the weights are proportional to the inverse of the order of the automorphism group of the lattice. For the constant terms this is essentially the Smith–Minkowski–Siegel mass formula.

References

• Siegel, Carl Ludwig (1951), "Indefinite quadratische Formen und Funktionentheorie. I", Mathematische Annalen 124: 17–54, doi:10.1007/BF01343549, ISSN 0025-5831 
• Siegel, Carl Ludwig (1952), "Indefinite quadratische Formen und Funktionentheorie. II", Mathematische Annalen 124: 364–387, doi:10.1007/BF01343576, ISSN 0025-5831 
• Weil, André (1964), "Sur certains groupes d'opérateurs unitaires", Acta Mathematica 111: 143–211, doi:10.1007/BF02391012, ISSN 0001-5962 
• Weil, André (1965), "Sur la formule de Siegel dans la théorie des groupes classiques", Acta Mathematica 113: 1–87, doi:10.1007/BF02391774, ISSN 0001-5962