Siegel–Weil formula

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.

(1951), "Indefinite quadratische Formen und Funktionentheorie. I", Mathematische Annalen, 124: 17–54, doi:10.1007/BF01343549, ISSN 0025-5831, MR 0067930, S2CID 121216201

Siegel, Carl Ludwig

(1952), "Indefinite quadratische Formen und Funktionentheorie. II", Mathematische Annalen, 124: 364–387, doi:10.1007/BF01343576, ISSN 0025-5831, MR 0067931, S2CID 179177878

Siegel, Carl Ludwig

(1964), "Sur certains groupes d'opérateurs unitaires", Acta Mathematica, 111: 143–211, doi:10.1007/BF02391012, ISSN 0001-5962, MR 0165033

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, MR 0223373