hasEulerProduct
P96490
predicate
Indicates that a mathematical function or object can be expressed as an infinite product over prime numbers (an Euler product), typically reflecting a multiplicative structure.
All labels observed (2)
| Label | Occurrences |
|---|---|
| hasEulerProduct canonical | 3 |
| canHaveEulerProduct | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: hasEulerProduct
Generated description
Indicates that a mathematical function or object can be expressed as an infinite product over prime numbers (an Euler product), typically reflecting a multiplicative structure.
Sample triples (4)
| Subject | Object |
|---|---|
| Dirichlet L-functions | L(s,χ)=∏_{p}(1−χ(p)p^{-s})^{-1} for Re(s)>1 ⓘ |
|
Dedekind zeta functions
surface form:
Dedekind zeta function
|
product over prime ideals ⓘ |
| Dirichlet series | when coefficients are multiplicative via predicate surface "canHaveEulerProduct" ⓘ |
| Selberg zeta function | over primitive closed geodesics ⓘ |