Orthogonal and symplectic n-level densities /

"In this paper we apply to the zeros of families of L-functions with orthogonal or symplectic symmetry the method that Conrey and Snaith (Correlations of eigenvalues and Riemann zeros, 2008) used to calculate the n-correlation of the zeros of the Riemann zeta function. This method uses the Rati...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Mason, A. M. (Amy Marie), 1985- (Autor), Snaith, N. C. (Nina C.) (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, RI : American Mathematical Society, [2018]
Colección:Memoirs of the American Mathematical Society ; no. 1194.
Temas:
L-functions.
Orthogonalization methods.
Symplectic and contact topology.
Number theory.
Numerical analysis.
Fonctions L.
Méthodes d'orthogonalisation.
Topologie symplectique et de contact.
Théorie des nombres.
Analyse numérique.
Análisis numérico
Toería de números
L-functions
Number theory
Numerical analysis
Orthogonalization methods
Symplectic and contact topology
Acceso en línea:Texto completo
Descripción
Sumario:"In this paper we apply to the zeros of families of L-functions with orthogonal or symplectic symmetry the method that Conrey and Snaith (Correlations of eigenvalues and Riemann zeros, 2008) used to calculate the n-correlation of the zeros of the Riemann zeta function. This method uses the Ratios Conjectures (Conrey, Farmer, and Zimbauer, 2008) for averages of ratios of zeta or L-functions. Katz and Sarnak (Zeroes of zeta functions and symmetry, 1999) conjecture that the zero statistics of families of L-functions have an underlying symmetry relating to one of the classical compact groups U(N), O(N) and USp(2N). Here we complete the work already done with U(N) (Conrey and Snaith, Correlations of eigenvalues and Riemann zeros, 2008) to show how new methods for calculating the n-level densities of eigenangles of random orthogonal or symplectic matrices can be used to create explicit conjectures for the n-level densities of zeros of L-functions with orthogonal or symplectic symmetry, including all the lower order terms. We show how the method used here results in formulae that are easily modified when the test function used has a restricted range of support, and this will facilitate comparison with rigorous number theoretic n-level density results."--Page v.
Notas:"January 2018, volume 251, number 1194 (first of 6 numbers)."
Descripción Física:1 online resource (v, 93 pages) : illustrations
Bibliografía:Includes bibliographical references (pages 89-93).
ISBN:9781470442620
1470442620
ISSN:0065-9266 ;

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