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Fungrim entry: 458198

χ(0)={1,q=10,q≠1\chi(0) = \begin{cases} 1, & q = 1\\0, & q \ne 1\\ \end{cases}
Assumptions:q∈Z≥1  and⁡  χ∈Gqq \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \chi \in G_{q}
TeX:
\chi(0) = \begin{cases} 1, & q = 1\\0, & q \ne 1\\ \end{cases}

q \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \chi \in G_{q}
Definitions:
Fungrim symbol Notation Short description
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
DirichletGroupGqG_{q} Dirichlet characters with given modulus
Source code for this entry:
Entry(ID("458198"),
    Formula(Equal(chi(0), Cases(Tuple(1, Equal(q, 1)), Tuple(0, NotEqual(q, 1))))),
    Variables(q, chi),
    Assumptions(And(Element(q, ZZGreaterEqual(1)), Element(chi, DirichletGroup(q)))))

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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