The completed Dirichlet L-function is an entire function of s. It is defined by b788a1 and taking the limiting value at the exceptional points s
where a pole appears in one of the constituent factors.
In the literature, this function is sometimes multiplied by a different constant factor (depending on χ
but constant with respect to s
).
Definitions:
| Fungrim symbol | Notation | Short description |
|---|---|---|
| DirichletLambda | Λ(s,χ) | Completed Dirichlet L-function |
Source code for this entry:
Entry(ID("cc6a5a"),
SymbolDefinition(DirichletLambda, DirichletLambda(s, chi), "Completed Dirichlet L-function"),
Description("The completed Dirichlet L-function is an entire function of", s, ".", "It is defined by", EntryReference("b788a1"), "and taking the limiting value at the exceptional points", s, "where a pole appears in one of the constituent factors."),
Description("In the literature, this function is sometimes multiplied by a different constant factor (depending on", chi, "but constant with respect to", s, ")."))