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Fungrim entry: 50adea

L ⁣(s,χ)=L ⁣(s,χ)L\!\left(\overline{s}, \chi\right) = \overline{L\!\left(s, \overline{\chi}\right)}
Assumptions:qZ1  and  χGq  and  sCq \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \chi \in G_{q} \;\mathbin{\operatorname{and}}\; s \in \mathbb{C}
L\!\left(\overline{s}, \chi\right) = \overline{L\!\left(s, \overline{\chi}\right)}

q \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \chi \in G_{q} \;\mathbin{\operatorname{and}}\; s \in \mathbb{C}
Fungrim symbol Notation Short description
DirichletLL ⁣(s,χ)L\!\left(s, \chi\right) Dirichlet L-function
Conjugatez\overline{z} Complex conjugate
CCC\mathbb{C} Complex numbers
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
DirichletGroupGqG_{q} Dirichlet characters with given modulus
Source code for this entry:
    Formula(Equal(DirichletL(Conjugate(s), chi), Conjugate(DirichletL(s, Conjugate(chi))))),
    Variables(s, CC),
    Assumptions(And(Element(q, ZZGreaterEqual(1)), Element(chi, DirichletGroup(q)), Element(s, CC))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC