Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Mathematical series
|
| gptkbp:defines |
A Dirichlet series is an infinite series of the form \\( \\sum_{n=1}^{\\infty} \\frac{a_n}{n^s} \\), where \\( a_n \\) are complex numbers and \\( s \\) is a complex variable.
|
| gptkbp:example |
gptkb:lion
gptkb:Riemann_zeta_function |
| gptkbp:field |
gptkb:Mathematics
gptkb:Number_theory Complex analysis |
| gptkbp:hasSpecialCase |
Generalized Dirichlet series
|
| https://www.w3.org/2000/01/rdf-schema#label |
Dirichlet-Reihen
|
| gptkbp:language |
gptkb:German
|
| gptkbp:namedAfter |
gptkb:Peter_Gustav_Lejeune_Dirichlet
|
| gptkbp:property |
Converges absolutely for \\( \\Re(s) > \\sigma_c \\), where \\( \\sigma_c \\) is the abscissa of convergence.
Can be analytically continued in some cases. |
| gptkbp:relatedTo |
gptkb:Euler_product
Multiplicative functions |
| gptkbp:usedIn |
gptkb:Analytic_number_theory
|
| gptkbp:bfsParent |
gptkb:Riemannsche_Zeta-Funktion
|
| gptkbp:bfsLayer |
7
|