Assumptions:
TeX:
L\!\left(s, \chi_{q \, . \, 1}\right) = \zeta\!\left(s\right) \prod_{p \mid q} \left(1 - \frac{1}{{p}^{s}}\right) q \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; s \in \mathbb{C}
Definitions:
Fungrim symbol | Notation | Short description |
---|---|---|
DirichletL | Dirichlet L-function | |
DirichletCharacter | Dirichlet character | |
RiemannZeta | Riemann zeta function | |
PrimeProduct | Product over primes | |
Pow | Power | |
ZZGreaterEqual | Integers greater than or equal to n | |
CC | Complex numbers |
Source code for this entry:
Entry(ID("629f70"), Formula(Equal(DirichletL(s, DirichletCharacter(q, 1)), Mul(RiemannZeta(s), PrimeProduct(Parentheses(Sub(1, Div(1, Pow(p, s)))), For(p), Divides(p, q))))), Variables(q, s), Assumptions(And(Element(q, ZZGreaterEqual(1)), Element(s, CC))))