Fungrim entry: 97f631

\operatorname{EssentialSingularities}\!\left(L\!\left(s, \chi\right), s, \mathbb{C} \cup \left\{{\tilde \infty}\right\}\right) = \left\{{\tilde \infty}\right\}

Assumptions:

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

TeX:

\operatorname{EssentialSingularities}\!\left(L\!\left(s, \chi\right), s, \mathbb{C} \cup \left\{{\tilde \infty}\right\}\right) = \left\{{\tilde \infty}\right\}

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
`CC`	$\mathbb{C}$	Complex numbers
`UnsignedInfinity`	${\tilde \infty}$	Unsigned infinity
`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("97f631"),
    Formula(Equal(EssentialSingularities(DirichletL(s, chi), s, Union(CC, Set(UnsignedInfinity))), Set(UnsignedInfinity))),
    Variables(q, chi),
    Assumptions(And(Element(q, ZZGreaterEqual(1)), Element(chi, DirichletGroup(q)))))

Topics using this entry

Dirichlet L-functions