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Fungrim entry: b78a50

Gq ⁣(χ)=q\left|G_{q}\!\left(\chi\right)\right| = \sqrt{q}
Assumptions:qZ1  and  χGqPrimitiveq \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \chi \in G^{\text{Primitive}}_{q}
\left|G_{q}\!\left(\chi\right)\right| = \sqrt{q}

q \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \chi \in G^{\text{Primitive}}_{q}
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^{\text{Primitive}}_{q} Primitive Dirichlet characters with given modulus
Source code for this entry:
    Formula(Equal(Abs(GaussSum(q, chi)), Sqrt(q))),
    Variables(q, chi),
    Assumptions(And(Element(q, ZZGreaterEqual(1)), Element(chi, PrimitiveDirichletCharacters(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