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 Fq(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