Siegel mass formula
E871399
The Siegel mass formula is a fundamental result in number theory that relates the weighted count (mass) of quadratic forms in a given genus to special values of zeta and L-functions, providing deep connections between arithmetic and geometry.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Siegel mass formula canonical | 1 |
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theorem
ⓘ
result in number theory ⓘ |
| appliesTo |
genera of quadratic forms
ⓘ
lattices ⓘ quadratic forms ⓘ |
| characterizes | mass of a genus of quadratic forms ⓘ |
| concerns |
indefinite quadratic forms
ⓘ
integral quadratic forms ⓘ positive definite quadratic forms ⓘ rational quadratic forms ⓘ |
| connects |
arithmetic of quadratic forms and analytic number theory
ⓘ
global arithmetic invariants ⓘ local representation theory of quadratic forms ⓘ |
| field |
arithmetic geometry
ⓘ
arithmetic of quadratic forms ⓘ number theory ⓘ |
| formalism |
adelic orthogonal groups
ⓘ
orthogonal group of a quadratic space ⓘ |
| gives |
expression for mass as product of local factors
ⓘ
expression involving Dedekind zeta functions ⓘ expression involving Dirichlet L-functions ⓘ product formula for the mass of a genus ⓘ |
| hasGeneralization |
Tamagawa number formula for orthogonal groups
NERFINISHED
ⓘ
mass formula for hermitian forms ⓘ mass formula for quadratic lattices over number fields ⓘ |
| historicalPeriod | 20th century mathematics ⓘ |
| influenced |
development of the theory of Tamagawa numbers
ⓘ
modern theory of automorphic forms ⓘ |
| involves |
product of local densities at all primes
ⓘ
volume of quotient of orthogonal group ⓘ |
| isToolFor |
classification of quadratic forms
ⓘ
computation of class numbers of quadratic forms ⓘ study of lattices in Euclidean space ⓘ study of representation numbers of quadratic forms ⓘ |
| namedAfter | Carl Ludwig Siegel NERFINISHED ⓘ |
| provenBy | Carl Ludwig Siegel NERFINISHED ⓘ |
| relatedTo |
Minkowski–Siegel formula
NERFINISHED
ⓘ
Smith–Minkowski–Siegel mass formula NERFINISHED ⓘ Tamagawa measures NERFINISHED ⓘ theta correspondence ⓘ |
| relates |
masses of quadratic forms
ⓘ
special values of L-functions ⓘ special values of zeta functions ⓘ |
| usesConcept |
Eisenstein series
NERFINISHED
ⓘ
adelic methods ⓘ automorphism group of a quadratic form ⓘ equivalence classes of quadratic forms ⓘ genus of quadratic forms ⓘ local densities ⓘ theta series ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.