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Fungrim entry: 789ca4

L ⁣(0,χ)=1qk=1qkχ(k)L\!\left(0, \chi\right) = -\frac{1}{q} \sum_{k=1}^{q} k \chi(k)
Assumptions:qZ1  and  χGq  and  χχq.1q \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \chi \in G_{q} \;\mathbin{\operatorname{and}}\; \chi \ne \chi_{q \, . \, 1}
L\!\left(0, \chi\right) = -\frac{1}{q} \sum_{k=1}^{q} k \chi(k)

q \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \chi \in G_{q} \;\mathbin{\operatorname{and}}\; \chi \ne \chi_{q \, . \, 1}
Fungrim symbol Notation Short description
DirichletLL ⁣(s,χ)L\!\left(s, \chi\right) Dirichlet L-function
Sumnf(n)\sum_{n} f(n) Sum
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
DirichletGroupGqG_{q} Dirichlet characters with given modulus
DirichletCharacterχq.\chi_{q \, . \, \ell} Dirichlet character
Source code for this entry:
    Formula(Equal(DirichletL(0, chi), Mul(Neg(Div(1, q)), Sum(Mul(k, chi(k)), For(k, 1, q))))),
    Variables(chi, q),
    Assumptions(And(Element(q, ZZGreaterEqual(1)), Element(chi, DirichletGroup(q)), NotEqual(chi, DirichletCharacter(q, 1)))))

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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