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- Selberg_zeta_function abstract "The Selberg zeta-function was introduced by Atle Selberg (1956). It is analogous to the famous Riemann zeta function where is the set of prime numbers. The Selberg zeta-function uses the lengths of simple closed geodesics instead of the primes numbers. If is a subgroup of SL(2,R) Selberg zeta function is defined as follows,orwhere p run all over the prime congruent class and N(p) is the norm of congruent class p, which is square of the bigger eigenvalue of p.For any hyperbolic surface of finite area there is an associated Selberg zeta-function; this function is a meromorphic function defined in the complex plane. The zeta function is defined in terms of the closed geodesics of the surface.The zeros and poles of the Selberg zeta-function, Z(s), can be described in terms of spectral data of the surface.The zeros are at the following points: For every cusp form with eigenvalue there exists a zero at the point . The order of the zero equals the dimension of the corresponding eigenspace. (A cusp form is an eigenfunction to the Laplace-Beltrami operator which has Fourier expansion with zero constant term.) The zeta-function also has a zero at every pole of the determinant of the scattering matrix, . The order of the zero equals the order of the corresponding pole of the scattering matrix.The zeta-function also has poles at , and can have zeros or poles at the points .".
- Selberg_zeta_function wikiPageID "3680650".
- Selberg_zeta_function wikiPageRevisionID "569219303".
- Selberg_zeta_function authorlink "Atle Selberg".
- Selberg_zeta_function first "Atle".
- Selberg_zeta_function hasPhotoCollection Selberg_zeta_function.
- Selberg_zeta_function last "Selberg".
- Selberg_zeta_function year "1956".
- Selberg_zeta_function subject Category:Spectral_theory.
- Selberg_zeta_function subject Category:Zeta_and_L-functions.
- Selberg_zeta_function comment "The Selberg zeta-function was introduced by Atle Selberg (1956). It is analogous to the famous Riemann zeta function where is the set of prime numbers.".
- Selberg_zeta_function label "Fonction zêta de Selberg".
- Selberg_zeta_function label "Función zeta de Selberg".
- Selberg_zeta_function label "Selberg zeta function".
- Selberg_zeta_function label "دالة زيتا لسيلبرغ".
- Selberg_zeta_function label "セルバーグゼータ函数".
- Selberg_zeta_function sameAs Función_zeta_de_Selberg.
- Selberg_zeta_function sameAs Fonction_zêta_de_Selberg.
- Selberg_zeta_function sameAs セルバーグゼータ函数.
- Selberg_zeta_function sameAs m.09v3cs.
- Selberg_zeta_function sameAs Q3075282.
- Selberg_zeta_function sameAs Q3075282.
- Selberg_zeta_function wasDerivedFrom Selberg_zeta_function?oldid=569219303.
- Selberg_zeta_function isPrimaryTopicOf Selberg_zeta_function.