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Fungrim entry: 982e3b

0<Re ⁣(ρn,χ)<10 < \operatorname{Re}\!\left(\rho_{n, \chi}\right) < 1
Assumptions:qZ1andχGqprimitiveandnZandn0q \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \chi \in G_{q}^{\text{primitive}} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \ne 0
TeX:
0 < \operatorname{Re}\!\left(\rho_{n, \chi}\right) < 1

q \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \chi \in G_{q}^{\text{primitive}} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \ne 0
Definitions:
Fungrim symbol Notation Short description
ReRe ⁣(z)\operatorname{Re}\!\left(z\right) Real part
DirichletLZeroρn,χ\rho_{n, \chi} Nontrivial zero of Dirichlet L-function
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
PrimitiveDirichletCharactersGqprimitiveG_{q}^{\text{primitive}} Primitive Dirichlet characters with given modulus
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("982e3b"),
    Formula(Less(0, Re(DirichletLZero(n, chi)), 1)),
    Variables(q, n, chi),
    Assumptions(And(Element(q, ZZGreaterEqual(1)), Element(chi, PrimitiveDirichletCharacters(q)), Element(n, ZZ), Unequal(n, 0))))

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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