Fungrim entry: cc6a5a

Symbol: DirichletLambda —

\Lambda\!\left(s, \chi\right)

— Completed Dirichlet L-function

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

\chi

but constant with respect to

s

Definitions:

Fungrim symbol	Notation	Short description
`DirichletLambda`	$\Lambda\!\left(s, \chi\right)$	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, ")."))

Topics using this entry

Dirichlet L-functions