Fungrim home page

Fungrim entry: b78a50

Gq ⁣(χ)=q\left|G_{q}\!\left(\chi\right)\right| = \sqrt{q}
Assumptions:qZ1andχGqprimitiveq \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \chi \in G_{q}^{\text{primitive}}
TeX:
\left|G_{q}\!\left(\chi\right)\right| = \sqrt{q}

q \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \chi \in G_{q}^{\text{primitive}}
Definitions:
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
GaussSumGq ⁣(χ)G_{q}\!\left(\chi\right) Gauss sum
Sqrtz\sqrt{z} Principal square root
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
PrimitiveDirichletCharactersGqprimitiveG_{q}^{\text{primitive}} Primitive Dirichlet characters with given modulus
Source code for this entry:
Entry(ID("b78a50"),
    Formula(Equal(Abs(GaussSum(q, chi)), Sqrt(q))),
    Variables(q, chi),
    Assumptions(And(Element(q, ZZGreaterEqual(1)), Element(chi, PrimitiveDirichletCharacters(q)))))

Topics using this entry

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

2019-08-21 11:44:15.926409 UTC