Abstract
In this paper we demonstrate that the alternative form, derived by us in an earlier paper, of the nlevel densities for eigenvalues of matrices from the classical compact group USp(2N) is far better suited for comparison with derivations of the nlevel densities of zeros in the family of Dirichlet Lfunctions associated with real quadratic characters than the traditional determinantal random matrix formula. Previous authors have found ingenious proofs that the leading order term of the nlevel density of the zeros agrees with the determinantal random matrix result under certain conditions, but here we show that comparison is more straightforward if the more suitable form of the random matrix result is used. For the support of the test function in [1,1] and in [2,2] we compare with existing number theoretical results. For support in [3,3] no rigorous number theoretical result is known for the nlevel densities, but we derive the densities here using random matrix theory in the hope that this may make the path to a rigorous number theoretical result clearer.
Original language  English 

Article number  1650013 
Number of pages  36 
Journal  Random Matrices: Theory and Applications 
Volume  5 
Issue number  4 
Early online date  20 Oct 2016 
DOIs  
Publication status  Published  Oct 2016 
Keywords
 Random matrix theory
 Dirichlet Lfunctions
 nlevel densities
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Professor Nina C Snaith
 School of Mathematics  Professor of Mathematical Physics
 Applied Mathematics
 Mathematical Physics
 Pure Mathematics
Person: Academic , Member