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Fungrim entry: ff8254

L ⁣(s,χ2n(1,))=(12s)ζ ⁣(s)L\!\left(s, \chi_{{2}^{n}}(1, \cdot)\right) = \left(1 - {2}^{-s}\right) \zeta\!\left(s\right)
Assumptions:nZ1andsCn \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, s \in \mathbb{C}
TeX:
L\!\left(s, \chi_{{2}^{n}}(1, \cdot)\right) = \left(1 - {2}^{-s}\right) \zeta\!\left(s\right)

n \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, s \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
DirichletLL ⁣(s,χ)L\!\left(s, \chi\right) Dirichlet L-function
DirichletCharacterχq(,)\chi_{q}(\ell, \cdot) Dirichlet character
Powab{a}^{b} Power
RiemannZetaζ ⁣(s)\zeta\!\left(s\right) Riemann zeta function
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("ff8254"),
    Formula(Equal(DirichletL(s, DirichletCharacter(Pow(2, n), 1)), Mul(Sub(1, Pow(2, Neg(s))), RiemannZeta(s)))),
    Variables(n, s),
    Assumptions(And(Element(n, ZZGreaterEqual(1)), 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.

2019-08-21 11:44:15.926409 UTC