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- Generalized_Riemann_hypothesis abstract "The Riemann hypothesis is one of the most important conjectures in mathematics. It is a statement about the zeros of the Riemann zeta function. Various geometrical and arithmetical objects can be described by so-called global L-functions, which are formally similar to the Riemann zeta-function. One can then ask the same question about the zeros of these L-functions, yielding various generalizations of the Riemann hypothesis. Many mathematicians believe these generalizations of the Riemann hypothesis to be true. The only cases of these conjectures which have been proven occur in the function field case (not the number field case).Global L-functions can be associated to elliptic curves, number fields (in which case they are called Dedekind zeta-functions), Maass forms, and Dirichlet characters (in which case they are called Dirichlet L-functions). When the Riemann hypothesis is formulated for Dedekind zeta-functions, it is known as the extended Riemann hypothesis (ERH) and when it is formulated for Dirichlet L-functions, it is known as the generalized Riemann hypothesis (GRH). These two statements will be discussed in more detail below. (Many mathematicians use the label generalized Riemann hypothesis to cover the extension of the Riemann hypothesis to all global L-functions, not just the special case of Dirichlet L-functions.)".
- Generalized_Riemann_hypothesis wikiPageID "152567".
- Generalized_Riemann_hypothesis wikiPageRevisionID "588374984".
- Generalized_Riemann_hypothesis hasPhotoCollection Generalized_Riemann_hypothesis.
- Generalized_Riemann_hypothesis id "R/r081940".
- Generalized_Riemann_hypothesis title "Riemann hypothesis, generalized".
- Generalized_Riemann_hypothesis subject Category:Algebraic_geometry.
- Generalized_Riemann_hypothesis subject Category:Conjectures.
- Generalized_Riemann_hypothesis subject Category:Zeta_and_L-functions.
- Generalized_Riemann_hypothesis type Abstraction100002137.
- Generalized_Riemann_hypothesis type Cognition100023271.
- Generalized_Riemann_hypothesis type Concept105835747.
- Generalized_Riemann_hypothesis type Conjectures.
- Generalized_Riemann_hypothesis type Content105809192.
- Generalized_Riemann_hypothesis type Hypothesis105888929.
- Generalized_Riemann_hypothesis type Idea105833840.
- Generalized_Riemann_hypothesis type PsychologicalFeature100023100.
- Generalized_Riemann_hypothesis type Speculation105891783.
- Generalized_Riemann_hypothesis comment "The Riemann hypothesis is one of the most important conjectures in mathematics. It is a statement about the zeros of the Riemann zeta function. Various geometrical and arithmetical objects can be described by so-called global L-functions, which are formally similar to the Riemann zeta-function. One can then ask the same question about the zeros of these L-functions, yielding various generalizations of the Riemann hypothesis.".
- Generalized_Riemann_hypothesis label "Generalized Riemann hypothesis".
- Generalized_Riemann_hypothesis label "Hipótese generalizada de Riemann".
- Generalized_Riemann_hypothesis label "Hipótesis generalizada de Riemann".
- Generalized_Riemann_hypothesis label "Hypothèse de Riemann généralisée".
- Generalized_Riemann_hypothesis label "Ipotesi di Riemann generalizzata".
- Generalized_Riemann_hypothesis label "一般化されたリーマン予想".
- Generalized_Riemann_hypothesis label "广义黎曼猜想".
- Generalized_Riemann_hypothesis sameAs Hipótesis_generalizada_de_Riemann.
- Generalized_Riemann_hypothesis sameAs Hypothèse_de_Riemann_généralisée.
- Generalized_Riemann_hypothesis sameAs Ipotesi_di_Riemann_generalizzata.
- Generalized_Riemann_hypothesis sameAs 一般化されたリーマン予想.
- Generalized_Riemann_hypothesis sameAs 일반화_리만_가설.
- Generalized_Riemann_hypothesis sameAs Hipótese_generalizada_de_Riemann.
- Generalized_Riemann_hypothesis sameAs m.013wyj.
- Generalized_Riemann_hypothesis sameAs Q685140.
- Generalized_Riemann_hypothesis sameAs Q685140.
- Generalized_Riemann_hypothesis sameAs Generalized_Riemann_hypothesis.
- Generalized_Riemann_hypothesis wasDerivedFrom Generalized_Riemann_hypothesis?oldid=588374984.
- Generalized_Riemann_hypothesis isPrimaryTopicOf Generalized_Riemann_hypothesis.