Integral moments of L-functions

2005/06/22 by J. Brian Conrey, J. B. Conrey, D. W. Farmer +5 · 37 citations
Mathematics · #Analytic Number Theory Research #Advanced Algebra and Geometry #Advanced Mathematical Identities

paper · doi:10.1112/s0024611504015175

Abstract

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 modelled using Random Matrix Theory. Numerical examples show good agreement with our conjectures. 2000 Mathematics Subject Classification 11M26, 15A52.

Citations

• Nonvanishing of Quadratic Dirichlet L-Functions at S = &#189

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