Dirichletsche L-Funktionen

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:mathematical_concept
gptkbp:category	L-functions
gptkbp:convergesTo	Re(s) > 1
gptkbp:domain	complex numbers
gptkbp:field	number theory
gptkbp:generalizes	gptkb:Riemann_zeta_function
gptkbp:hasAnalyticContinuation	yes
gptkbp:hasApplication	class number formula distribution of primes in arithmetic progressions non-vanishing at s=1 for non-principal character
gptkbp:hasEquation	yes
gptkbp:hasEulerProduct	L(s,χ) = ∏_{p prime} (1 - χ(p)p^{-s})^{-1}
gptkbp:hasSeriesRepresentation	L(s,χ) = Σ_{n=1}^∞ χ(n)/n^s
gptkbp:hasSpecialCase	Riemann zeta function (χ trivial)
https://www.w3.org/2000/01/rdf-schema#label	Dirichletsche L-Funktionen
gptkbp:languageOfOrigin	gptkb:German
gptkbp:namedAfter	gptkb:Peter_Gustav_Lejeune_Dirichlet
gptkbp:parameter	gptkb:Dirichlet_character_χ
gptkbp:relatedTo	gptkb:lion gptkb:prime_number_theorem_for_arithmetic_progressions modular forms automorphic forms
gptkbp:studiedBy	gptkb:Peter_Gustav_Lejeune_Dirichlet
gptkbp:subclassOf	L-functions
gptkbp:usedIn	analytic number theory proof of Dirichlet's theorem on arithmetic progressions
gptkbp:variant	complex variable s
gptkbp:bfsParent	gptkb:Riemannsche_Zeta-Funktion
gptkbp:bfsLayer	7