# Fungrim entry: 3ab92d

$\sum_{\chi \in G_{q}} \chi\!\left(n\right) = \begin{cases} \varphi\!\left(q\right), & n \equiv 1 \pmod {q}\\0, & \text{otherwise}\\ \end{cases}$
Assumptions:$q \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}$
TeX:
\sum_{\chi \in G_{q}} \chi\!\left(n\right) = \begin{cases} \varphi\!\left(q\right), & n \equiv 1 \pmod {q}\\0, & \text{otherwise}\\ \end{cases}

q \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
Sum$\sum_{n} f\!\left(n\right)$ Sum
DirichletGroup$G_{q}$ Dirichlet characters with given modulus
Totient$\varphi\!\left(n\right)$ Euler totient function
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
ZZ$\mathbb{Z}$ Integers
Source code for this entry:
Entry(ID("3ab92d"),
Formula(Equal(Sum(chi(n), chi, Element(chi, DirichletGroup(q))), Cases(Tuple(Totient(q), CongruentMod(n, 1, q)), Tuple(0, Otherwise)))),
Variables(q, n),
Assumptions(And(Element(q, ZZGreaterEqual(1)), Element(n, ZZ))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-17 11:32:46.829430 UTC