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- Atkin–Lehner_theory abstract "In mathematics, Atkin–Lehner theory is part of the theory of modular forms, in which the concept of newform is defined in such a way that the theory of Hecke operators can be extended to higher level. A newform is a cusp form 'new' at a given level N, where the levels are the nested subgroupsΓ0(N)of the modular group, with N ordered by divisibility. That is, if M divides N, Γ0(N) is a subgroup of Γ0(M). The oldforms for Γ0(N) are those modular forms f(τ) of level N of the form g(d τ) for modular forms g of level M with M a proper divisor of N, where d divides N/M. The newforms are defined as a vector subspace of the modular forms of level N, complementary to the space spanned by the oldforms, i.e. the orthogonal space with respect to the Petersson inner product.The Hecke operators, which act on the space of all cusp forms, preserve the subspace of newforms and are self-adjoint and commuting operators (with respect to the Petersson inner product) when restricted to this subspace. Therefore, the algebra of operators on newforms they generate is a finite-dimensional C*-algebra that is commutative; and by the spectral theory of such operators, there exists a basis for the space of newforms consisting of eigenforms for the full Hecke algebra.".
- Atkin–Lehner_theory wikiPageID "7483985".
- Atkin–Lehner_theory wikiPageLength "3666".
- Atkin–Lehner_theory wikiPageOutDegree "20".
- Atkin–Lehner_theory wikiPageRevisionID "707280016".
- Atkin–Lehner_theory wikiPageWikiLink C*-algebra.
- Atkin–Lehner_theory wikiPageWikiLink Category:Modular_forms.
- Atkin–Lehner_theory wikiPageWikiLink Congruence_subgroup.
- Atkin–Lehner_theory wikiPageWikiLink Cusp_form.
- Atkin–Lehner_theory wikiPageWikiLink Divisibility_rule.
- Atkin–Lehner_theory wikiPageWikiLink European_Mathematical_Society.
- Atkin–Lehner_theory wikiPageWikiLink Hecke_algebra.
- Atkin–Lehner_theory wikiPageWikiLink Hecke_operator.
- Atkin–Lehner_theory wikiPageWikiLink Involution_(mathematics).
- Atkin–Lehner_theory wikiPageWikiLink Koichiro_Harada.
- Atkin–Lehner_theory wikiPageWikiLink Mathematische_Annalen.
- Atkin–Lehner_theory wikiPageWikiLink Modular_form.
- Atkin–Lehner_theory wikiPageWikiLink Modular_group.
- Atkin–Lehner_theory wikiPageWikiLink Normal_subgroup.
- Atkin–Lehner_theory wikiPageWikiLink Petersson_inner_product.
- Atkin–Lehner_theory wikiPageWikiLink Self-adjoint_operator.
- Atkin–Lehner_theory wikiPageWikiLink Special_linear_group.
- Atkin–Lehner_theory wikiPageWikiLink Spectral_theorem.
- Atkin–Lehner_theory wikiPageWikiLink Subgroup.
- Atkin–Lehner_theory wikiPageWikiLinkText "Atkin–Lehner theory".
- Atkin–Lehner_theory wikiPageUsesTemplate Template:Citation.
- Atkin–Lehner_theory wikiPageUsesTemplate Template:Mr.
- Atkin–Lehner_theory wikiPageUsesTemplate Template:Reflist.
- Atkin–Lehner_theory subject Category:Modular_forms.
- Atkin–Lehner_theory hypernym Part.
- Atkin–Lehner_theory type Redirect.
- Atkin–Lehner_theory comment "In mathematics, Atkin–Lehner theory is part of the theory of modular forms, in which the concept of newform is defined in such a way that the theory of Hecke operators can be extended to higher level. A newform is a cusp form 'new' at a given level N, where the levels are the nested subgroupsΓ0(N)of the modular group, with N ordered by divisibility. That is, if M divides N, Γ0(N) is a subgroup of Γ0(M).".
- Atkin–Lehner_theory label "Atkin–Lehner theory".
- Atkin–Lehner_theory sameAs Q4815938.
- Atkin–Lehner_theory sameAs m.026343g.
- Atkin–Lehner_theory sameAs Atkin–Lehnerteori.
- Atkin–Lehner_theory sameAs Q4815938.
- Atkin–Lehner_theory wasDerivedFrom Atkin–Lehner_theory?oldid=707280016.
- Atkin–Lehner_theory isPrimaryTopicOf Atkin–Lehner_theory.