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Fungrim entry: ff8254

L ⁣(s,χ2n.1)=(12s)ζ ⁣(s)L\!\left(s, \chi_{{2}^{n} \, . \, 1}\right) = \left(1 - {2}^{-s}\right) \zeta\!\left(s\right)
Assumptions:nZ1  and  sCn \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; s \in \mathbb{C}
L\!\left(s, \chi_{{2}^{n} \, . \, 1}\right) = \left(1 - {2}^{-s}\right) \zeta\!\left(s\right)

n \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; s \in \mathbb{C}
Fungrim symbol Notation Short description
DirichletLL ⁣(s,χ)L\!\left(s, \chi\right) Dirichlet L-function
DirichletCharacterχq.\chi_{q \, . \, \ell} 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:
    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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2021-03-15 19:12:00.328586 UTC