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Fungrim entry: 982e3b

0<Re ⁣(ρn,χ)<10 < \operatorname{Re}\!\left(\rho_{n,\chi}\right) < 1
Assumptions:qZ1  and  χGqPrimitive  and  nZ  and  n0q \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \chi \in G^{\text{Primitive}}_{q} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; n \ne 0
0 < \operatorname{Re}\!\left(\rho_{n,\chi}\right) < 1

q \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \chi \in G^{\text{Primitive}}_{q} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; n \ne 0
Fungrim symbol Notation Short description
ReRe(z)\operatorname{Re}(z) 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^{\text{Primitive}}_{q} Primitive Dirichlet characters with given modulus
ZZZ\mathbb{Z} Integers
Source code for this entry:
    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), NotEqual(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.

2021-03-15 19:12:00.328586 UTC