Siegel–Weil formula

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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.


  • Siegel, Carl Ludwig (1951), "Indefinite quadratische Formen und Funktionentheorie. I", Mathematische Annalen, 124: 17–54, doi:10.1007/BF01343549, ISSN 0025-5831, MR 0067930
  • Siegel, Carl Ludwig (1952), "Indefinite quadratische Formen und Funktionentheorie. II", Mathematische Annalen, 124: 364–387, doi:10.1007/BF01343576, ISSN 0025-5831, MR 0067931
  • Weil, André (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