## Abstract

There has recently been interest in relating properties of matrices drawn at random from the classical compact groups to statistical characteristics of number-theoretical L-functions. One example is the relationship conjectured to hold between the value distributions of the characteristic polynomials of such matrices and value distributions within families of L-functions. These connections are extended here to non-classical groups. We focus on an explicit example: the exceptional Lie group G_{2}. The value distributions for characteristic polynomials associated with the 7- and 14-dimensional representations of G_{2}, defined with respect to the uniform invariant (Haar) measure, are calculated using two of the Macdonald constant term identities. A one-parameter family of L-functions over a finite field is described whose value distribution in the limit as the size of the finite field grows is related to that of the characteristic polynomials associated with the seven-dimensional representation of G_{2}. The random matrix calculations extend to all exceptional Lie groups.

Original language | English |
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Pages (from-to) | 2933-2944 |

Number of pages | 12 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 36 |

Issue number | 12 SPEC. ISS. |

DOIs | |

State | Published - 28 Mar 2003 |