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• Selberg_trace_formula abstract "In mathematics, the Selberg trace formula, introduced by Selberg (1956), is an expression for the character of the unitary representation of G on the space L2(G/Γ) of square-integrable functions, where G is a Lie group and Γ a cofinite discrete group. The character is given by the trace of certain functions on G.The simplest case is when Γ is cocompact, when the representation breaks up into discrete summands. Here the trace formula is an extension of the Frobenius formula for the character of an induced representation of finite groups. When Γ is the cocompact subgroup Z of the real numbers G = R, the Selberg trace formula is essentially the Poisson summation formula.The case when G/Γ is not compact is harder, because there is a continuous spectrum, described using Eisenstein series. Selberg worked out the non-compact case when G is the group SL(2, R); the extension to higher rank groups is the Arthur-Selberg trace formula.When Γ is the fundamental group of a Riemann surface, the Selberg trace formula describes the spectrum of differential operators such as the Laplacian in terms of geometric data involving the lengths of geodesics on the Riemann surface. In this case the Selberg trace formula is formally similar to the explicit formulas relating the zeros of the Riemann zeta function to prime numbers, with the zeta zeros corresponding to eigenvalues of the Laplacian, and the primes corresponding to geodesics. Motivated by the analogy, Selberg introduced the Selberg zeta function of a Riemann surface, whose analytic properties are encoded by the Selberg trace formula.".
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• Selberg_trace_formula wikiPageWikiLink Unitary_representation.
• Selberg_trace_formula wikiPageWikiLink Upper_half-plane.
• Selberg_trace_formula wikiPageWikiLinkText "Selberg trace formula".
• Selberg_trace_formula wikiPageWikiLinkText "trace formula".
• Selberg_trace_formula wikiPageUsesTemplate Template:!.
• Selberg_trace_formula wikiPageUsesTemplate Template:=.
• Selberg_trace_formula wikiPageUsesTemplate Template:Citation.
• Selberg_trace_formula wikiPageUsesTemplate Template:Harvtxt.
• Selberg_trace_formula wikiPageUsesTemplate Template:Math.
• Selberg_trace_formula wikiPageUsesTemplate Template:Mvar.
• Selberg_trace_formula wikiPageUsesTemplate Template:Sfrac.
• Selberg_trace_formula subject Category:Automorphic_forms.
• Selberg_trace_formula hypernym Expression.
• Selberg_trace_formula type Group.
• Selberg_trace_formula type Organisation.
• Selberg_trace_formula type Group.
• Selberg_trace_formula comment "In mathematics, the Selberg trace formula, introduced by Selberg (1956), is an expression for the character of the unitary representation of G on the space L2(G/Γ) of square-integrable functions, where G is a Lie group and Γ a cofinite discrete group. The character is given by the trace of certain functions on G.The simplest case is when Γ is cocompact, when the representation breaks up into discrete summands.".
• Selberg_trace_formula label "Selberg trace formula".
• Selberg_trace_formula sameAs Q3077649.
• Selberg_trace_formula sameAs Formule_des_traces_de_Selberg.
• Selberg_trace_formula sameAs セルバーグ跡公式.
• Selberg_trace_formula sameAs m.03wfr6.
• Selberg_trace_formula sameAs Q3077649.
• Selberg_trace_formula sameAs 塞爾伯格跡公式.
• Selberg_trace_formula wasDerivedFrom Selberg_trace_formula?oldid=694815201.
• Selberg_trace_formula isPrimaryTopicOf Selberg_trace_formula.