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Fungrim entry: fad52f

(χ(−1)=1)    ⟹    (L ⁣(0,χ)=0)\left(\chi(-1) = 1\right) \;\implies\; \left(L\!\left(0, \chi\right) = 0\right)
Assumptions:q∈Z≥2  and⁡  χ∈Gqq \in \mathbb{Z}_{\ge 2} \;\mathbin{\operatorname{and}}\; \chi \in G_{q}
TeX:
\left(\chi(-1) = 1\right) \;\implies\; \left(L\!\left(0, \chi\right) = 0\right)

q \in \mathbb{Z}_{\ge 2} \;\mathbin{\operatorname{and}}\; \chi \in G_{q}
Definitions:
Fungrim symbol Notation Short description
DirichletLL ⁣(s,χ)L\!\left(s, \chi\right) Dirichlet L-function
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
DirichletGroupGqG_{q} Dirichlet characters with given modulus
Source code for this entry:
Entry(ID("fad52f"),
    Formula(Implies(Equal(chi(-1), 1), Equal(DirichletL(0, chi), 0))),
    Variables(chi, q),
    Assumptions(And(Element(q, ZZGreaterEqual(2)), Element(chi, DirichletGroup(q)))))

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2021-03-15 19:12:00.328586 UTC