Fungrim home page

Fungrim entry: f7a866

B0,χ={φ ⁣(q)q,χ=χq(1,)0,otherwiseB_{0,\chi} = \begin{cases} \frac{\varphi\!\left(q\right)}{q}, & \chi = \chi_{q}(1, \cdot)\\0, & \text{otherwise}\\ \end{cases}
Assumptions:qZ1andχGqq \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \chi \in G_{q}
TeX:
B_{0,\chi} = \begin{cases} \frac{\varphi\!\left(q\right)}{q}, & \chi = \chi_{q}(1, \cdot)\\0, & \text{otherwise}\\ \end{cases}

q \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \chi \in G_{q}
Definitions:
Fungrim symbol Notation Short description
GeneralizedBernoulliBBn,χB_{n,\chi} Generalized Bernoulli number
Totientφ ⁣(n)\varphi\!\left(n\right) Euler totient function
DirichletCharacterχq(,)\chi_{q}(\ell, \cdot) Dirichlet character
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
DirichletGroupGqG_{q} Dirichlet characters with given modulus
Source code for this entry:
Entry(ID("f7a866"),
    Formula(Equal(GeneralizedBernoulliB(0, chi), Cases(Tuple(Div(Totient(q), q), Equal(chi, DirichletCharacter(q, 1))), Tuple(0, Otherwise)))),
    Variables(q, chi),
    Assumptions(And(Element(q, ZZGreaterEqual(1)), Element(chi, DirichletGroup(q)))))

Topics using this entry

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

2019-08-17 11:32:46.829430 UTC