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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:analyticContinuation
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Yes
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gptkbp:application
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Distribution of prime numbers in arithmetic progressions
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gptkbp:category
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L-functions
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gptkbp:definedIn
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gptkb:lion
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gptkbp:field
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gptkb:Number_theory
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gptkbp:generalizes
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gptkb:Riemann_zeta_function
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gptkbp:hasEquation
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Yes
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gptkbp:hasEulerProduct
|
L(s, χ) = ∏_{p} (1 - χ(p)p^{-s})^{-1}
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gptkbp:hasSeriesRepresentation
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L(s, χ) = Σ_{n=1}^∞ χ(n) n^{-s}
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gptkbp:hasSpecialCase
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gptkb:Riemann_zeta_function_(when_χ_is_trivial)
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|
https://www.w3.org/2000/01/rdf-schema#label
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Dirichlet L-functions
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gptkbp:namedAfter
|
gptkb:Peter_Gustav_Lejeune_Dirichlet
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gptkbp:property
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Holomorphic for non-principal character
Meromorphic function
Simple pole at s=1 for principal character
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gptkbp:relatedTo
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gptkb:Artin_L-functions
gptkb:Dedekind_zeta_function
gptkb:Generalized_Riemann_hypothesis
gptkb:Automorphic_forms
gptkb:Modular_forms
|
|
gptkbp:studiedBy
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gptkb:Peter_Gustav_Lejeune_Dirichlet
|
|
gptkbp:studiedIn
|
L-function theory
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|
gptkbp:usedIn
|
gptkb:Prime_number_theorem_for_arithmetic_progressions
gptkb:Analytic_number_theory
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gptkbp:variant
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Complex variable s
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gptkbp:bfsParent
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gptkb:Hecke_L-functions
gptkb:Generalized_Riemann_Hypothesis
gptkb:Euler_Products
gptkb:Riemann_zeta_function_(when_χ_is_trivial)
|
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gptkbp:bfsLayer
|
5
|