Fungrim entry: a07d28

L\!\left(0, \chi_{q \, . \, 1}\right) = \begin{cases} -\frac{1}{2}, & q = 1\\0, & \text{otherwise}\\ \end{cases}

Assumptions:

q \in \mathbb{Z}_{\ge 1}

TeX:

L\!\left(0, \chi_{q \, . \, 1}\right) = \begin{cases} -\frac{1}{2}, & q = 1\\0, & \text{otherwise}\\ \end{cases}

q \in \mathbb{Z}_{\ge 1}

Definitions:

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

Source code for this entry:

Entry(ID("a07d28"),
    Formula(Equal(DirichletL(0, DirichletCharacter(q, 1)), Cases(Tuple(Neg(Div(1, 2)), Equal(q, 1)), Tuple(0, Otherwise)))),
    Variables(q),
    Assumptions(And(Element(q, ZZGreaterEqual(1)))))

Topics using this entry

Dirichlet L-functions

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