Fungrim entry: 5c4552

L\!\left(1, \chi\right) \notin \overline{\mathbb{Q}}

Assumptions:

q \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \chi \in G_{q}

References:

https://doi.org/10.4153/CJM-2010-078-9

TeX:

L\!\left(1, \chi\right) \notin \overline{\mathbb{Q}}

q \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \chi \in G_{q}

Definitions:

Fungrim symbol	Notation	Short description
`DirichletL`	$L\!\left(s, \chi\right)$	Dirichlet L-function
`AlgebraicNumbers`	$\overline{\mathbb{Q}}$	Algebraic numbers
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n
`DirichletGroup`	$G_{q}$	Dirichlet characters with given modulus

Source code for this entry:

Entry(ID("5c4552"),
    Formula(NotElement(DirichletL(1, chi), AlgebraicNumbers)),
    Variables(q, chi),
    Assumptions(And(Element(q, ZZGreaterEqual(1)), Element(chi, DirichletGroup(q)))),
    References("https://doi.org/10.4153/CJM-2010-078-9"))

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