Statements (60)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
mathematical function
|
| gptkbp:defines |
ζ(s) = 1^(-s) + 2^(-s) + 3^(-s) + ... for Re(s) > 1
|
| gptkbp:hasFunction |
ζ(s)_=_2^s_π^(s-1)_sin(πs/2)_ζ(1-s)
|
| gptkbp:hasGoals |
trivial zeros at negative even integers
non-trivial zeros in the critical strip |
| gptkbp:hasSpecialty |
ζ(0) = -1/2
ζ(1) diverges ζ(3)_is_known_as_Apéry's_constant ζ(2)_=_π^2/6 |
| gptkbp:hasTheme |
complex numbers
|
| https://www.w3.org/2000/01/rdf-schema#label |
Riemann's Zeta Function
|
| gptkbp:isActiveIn |
for Re(s) > 1 and has a meromorphic continuation
|
| gptkbp:isConnectedTo |
gptkb:Riemann_Hypothesis
|
| gptkbp:isImportantFor |
analytic number theory
|
| gptkbp:isNamedAfter |
gptkb:Bernhard_Riemann
|
| gptkbp:isRelatedTo |
modular forms
L-functions prime numbers Dirichlet series zeta function of a group zeta function of a variety zeta regularization zeta function of a number field zeta function of a topological space Euler's_product_formula |
| gptkbp:isStudiedIn |
algebraic geometry
mathematical physics mathematical analysis complex analysis |
| gptkbp:isUsedIn |
gptkb:quantum_computing
artificial intelligence cryptography theoretical physics image processing data analysis machine learning algorithm design computational mathematics information theory mathematical modeling number theory data mining signal processing graph theory network theory probability theory random matrix theory statistical mechanics analytic continuation numerical analysis combinatorics statistical inference pattern recognition error correction codes signal detection financial mathematics machine vision quantum_physics |
| gptkbp:isUtilizedFor |
all non-trivial zeros on the critical line Re(s) = 1/2
|
| gptkbp:technologyDomain |
complex numbers
|