On the third moment of L([Formula presented],χd) I: The rational function field case

Adrian Diaconu

doi:10.1016/j.jnt.2018.09.023

On the third moment of L([Formula presented],χ_d) I: The rational function field case

Adrian Diaconu

Mathematics

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9 Scopus citations

Abstract

In this note, we prove the existence of a secondary term in the asymptotic formula of the cubic moment of quadratic Dirichlet L-functions ∑d₀−monic&sq.freedeg⁡d₀=DL([Formula presented],χ_d₀)³ over rational function fields on the order of q^{[Formula presented]D}. This term is in perfect analogy with the x^{[Formula presented]}-term indicated in our joint work [18] for the corresponding asymptotic formula over the rationals.

Original language	English (US)
Pages (from-to)	1-42
Number of pages	42
Journal	Journal of Number Theory
Volume	198
DOIs	https://doi.org/10.1016/j.jnt.2018.09.023
State	Published - May 2019

Keywords

Cubic moment
Quadratic Dirichlet L-functions
Rational function fields
Weyl group multiple Dirichlet series

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AB - In this note, we prove the existence of a secondary term in the asymptotic formula of the cubic moment of quadratic Dirichlet L-functions ∑d0−monic&sq.freedeg⁡d0=DL([Formula presented],χd0 )3 over rational function fields on the order of q[Formula presented]D. This term is in perfect analogy with the x[Formula presented]-term indicated in our joint work [18] for the corresponding asymptotic formula over the rationals.

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KW - Rational function fields

KW - Weyl group multiple Dirichlet series

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