Integral moments of L-functions

JB Conrey, DW Farmer, JP Keating, MO Rubinstein, NC Snaith

Research output: Contribution to journalArticle (Academic Journal)peer-review

163 Citations (Scopus)


We give a new heuristic for all of the main terms in the integral moments of various families of primitive L-functions. 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 L-functions 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 contributionIntegral moments of L-functions
Original languageEnglish
Pages (from-to)33 - 104
Number of pages72
JournalProceedings of the London Mathematical Society
Volume91 (1)
Publication statusPublished - Jul 2005

Bibliographical note

Publisher: Cambridge University Press
Other identifier: IDS Number: 948MJ

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