Fungrim entry: ff8254

L\!\left(s, \chi_{{2}^{n} \, . \, 1}\right) = \left(1 - {2}^{-s}\right) \zeta\!\left(s\right)

Assumptions:

n \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; s \in \mathbb{C}

TeX:

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}

Definitions:

Fungrim symbol	Notation	Short description
`DirichletL`	$L\!\left(s, \chi\right)$	Dirichlet L-function
`DirichletCharacter`	$\chi_{q \, . \, \ell}$	Dirichlet character
`Pow`	${a}^{b}$	Power
`RiemannZeta`	$\zeta\!\left(s\right)$	Riemann zeta function
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n
`CC`	$\mathbb{C}$	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))))

Topics using this entry

Dirichlet L-functions