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- 4_conjecture abstract "In mathematics, Selberg's conjecture, conjectured by Selberg (1965, p. 13), states that the eigenvalues of the Laplace operator on Maass wave forms of congruence subgroups are at least 1/4. Selberg showed that the eigenvalues are at least 3/16. The generalized Ramanujan conjecture for the general linear group implies Selberg's conjecture. More precisely, Selberg's conjecture is essentially the generalized Ramanujan conjecture for the group GL2 over the rationals at the infinite place, and says that the component at infinity of the corresponding representation is a principal series representation of GL2(R) (rather than a complementary series representation). The generalized Ramanujan conjecture in turn follows from the Langlands functoriality conjecture, and this has led to some progress on Selberg's conjecture.".
- 4_conjecture wikiPageExternalLink books?id=6xAZAQAAIAAJ.
- 4_conjecture wikiPageID "32329601".
- 4_conjecture wikiPageLength "2029".
- 4_conjecture wikiPageOutDegree "11".
- 4_conjecture wikiPageRevisionID "644519561".
- 4_conjecture wikiPageWikiLink American_Mathematical_Society.
- 4_conjecture wikiPageWikiLink Category:Automorphic_forms.
- 4_conjecture wikiPageWikiLink Category:Conjectures.
- 4_conjecture wikiPageWikiLink Eigenvalues_and_eigenvectors.
- 4_conjecture wikiPageWikiLink General_linear_group.
- 4_conjecture wikiPageWikiLink Generalized_Ramanujan_conjecture.
- 4_conjecture wikiPageWikiLink Journal_of_the_American_Mathematical_Society.
- 4_conjecture wikiPageWikiLink Langlands_functoriality_conjecture.
- 4_conjecture wikiPageWikiLink Langlands_program.
- 4_conjecture wikiPageWikiLink Laplace_operator.
- 4_conjecture wikiPageWikiLink Maass_wave_form.
- 4_conjecture wikiPageWikiLink Mathematics.
- 4_conjecture wikiPageWikiLink Ramanujan–Petersson_conjecture.
- 4_conjecture wikiPageWikiLinkText "Selberg's 1/4 conjecture".
- 4_conjecture authorlink "Atle Selberg".
- 4_conjecture authorlink "Stephen Gelbart".
- 4_conjecture first "S.".
- 4_conjecture hasPhotoCollection 4_conjecture.
- 4_conjecture id "s/s130210".
- 4_conjecture last "Gelbart".
- 4_conjecture last "Selberg".
- 4_conjecture loc "p. 13".
- 4_conjecture wikiPageUsesTemplate Template:Citation.
- 4_conjecture wikiPageUsesTemplate Template:Eom.
- 4_conjecture wikiPageUsesTemplate Template:For.
- 4_conjecture wikiPageUsesTemplate Template:Harvs.
- 4_conjecture year "1965".
- 4_conjecture subject Category:Automorphic_forms.
- 4_conjecture subject Category:Conjectures.
- 4_conjecture comment "In mathematics, Selberg's conjecture, conjectured by Selberg (1965, p. 13), states that the eigenvalues of the Laplace operator on Maass wave forms of congruence subgroups are at least 1/4. Selberg showed that the eigenvalues are at least 3/16. The generalized Ramanujan conjecture for the general linear group implies Selberg's conjecture.".
- 4_conjecture label "Selberg's 1/4 conjecture".
- 4_conjecture sameAs セルバーグの予想.
- 4_conjecture sameAs m.0gjdrvy.
- 4_conjecture sameAs 4-förmodan.
- 4_conjecture sameAs Q7447522.
- 4_conjecture sameAs Q7447522.
- 4_conjecture wasDerivedFrom 4_conjectureoldid=644519561.
- 4_conjecture isPrimaryTopicOf 4_conjecture.