## Abstract

We establish the meromorphic continuation of a multiple Dirichlet series associated to the fourth moment of quadratic Dirichlet L-functions, over the rational function field F_{q}(T) with q odd, up to its natural boundary. This is the first such result in which the group of functional equations is infinite; in such cases, it is expected that the series cannot be continued everywhere but can at least be extended to a large enough region to deduce asymptotics at the central point. In this case, these asymptotics coincide with existing predictions for the fourth moment of the symplectic family of quadratic Dirichlet L-functions. The construction uses the Weyl group action of a particular Kac-Moody algebra; this suggests an approach to higher moments using appropriate non-affine Kac-Moody algebras.

Original language | English (US) |
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Pages (from-to) | 485-517 |

Number of pages | 33 |

Journal | Moscow Mathematical Journal |

Volume | 10 |

Issue number | 3 |

DOIs | |

State | Published - 2010 |

## Keywords

- Coxeter group
- Finite field
- Moments of quadratic dirichlet l-functions
- Multiple dirichlet series
- Rational function field
- Roots