Fungrim entry: 7c86d5

L\!\left(s, \overline{\chi}\right) = \overline{L\!\left(\overline{s}, \chi\right)}

Assumptions:

q \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \chi \in G_{q} \;\mathbin{\operatorname{and}}\; s \in \mathbb{C}

TeX:

L\!\left(s, \overline{\chi}\right) = \overline{L\!\left(\overline{s}, \chi\right)}

q \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \chi \in G_{q} \;\mathbin{\operatorname{and}}\; s \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`DirichletL`	$L\!\left(s, \chi\right)$	Dirichlet L-function
`Conjugate`	$\overline{z}$	Complex conjugate
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n
`DirichletGroup`	$G_{q}$	Dirichlet characters with given modulus
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("7c86d5"),
    Formula(Equal(DirichletL(s, Conjugate(chi)), Conjugate(DirichletL(Conjugate(s), chi)))),
    Variables(s, q, chi),
    Assumptions(And(Element(q, ZZGreaterEqual(1)), Element(chi, DirichletGroup(q)), Element(s, CC))))

Topics using this entry

Dirichlet L-functions