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Abstract
We give a new heuristic for all of the main terms in the integral moments of various families of primitive Lfunctions. The results agree with previous conjectures for the leading order terms. Our conjectures also have an almost identical form to exact expressions for the corresponding moments of the characteristic polynomials of either unitary, orthogonal, or symplectic matrices, where the moments are defined by the appropriate group averages. This lends support to the idea that arithmetical Lfunctions have a spectral interpretation, and that their value distributions can be modeled using Random Matrix Theory. Numerical examples show good agreement with our conjectures.
Translated title of the contribution  Integral moments of Lfunctions 

Original language  English 
Pages (fromto)  33  104 
Number of pages  72 
Journal  Proceedings of the London Mathematical Society 
Volume  91 (1) 
DOIs  
Publication status  Published  Jul 2005 
Bibliographical note
Publisher: Cambridge University PressOther identifier: IDS Number: 948MJ
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Projects
 1 Finished

VALUES OF LFUNCTIONS & RANDOM MATRIX THEORY  SENIOR FELLOWSHIP
French, P. E.
1/10/04 → 1/10/09
Project: Research