Dirichlet series
C11530
concept
A Dirichlet series is an infinite series of the form ∑ₙ₌₁^∞ aₙ n^(-s), where s is a complex variable and aₙ are complex coefficients, used extensively in analytic number theory to study arithmetic functions and L-functions.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Dirichlet series canonical | 4 |
| class of Dirichlet series | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: Dirichlet series
Generated description
A Dirichlet series is an infinite series of the form ∑ₙ₌₁^∞ aₙ n^(-s), where s is a complex variable and aₙ are complex coefficients, used extensively in analytic number theory to study arithmetic functions and L-functions.
Instances (5)
| Instance | Via concept surface |
|---|---|
| Selberg class | class of Dirichlet series |
|
Dedekind zeta functions
surface form:
Dedekind zeta function
|
— |
| Dirichlet eta function | — |
| Riemann zeta function | — |
| Hurwitz zeta function | — |