On the third moment of \(L(\frac{1}{2}, \chi_d)\). I: The rational function field case

DOI10.1016/j.jnt.2018.09.023zbMath1443.11164arXiv1801.00486OpenAlexW2896753462MaRDI QIDQ1710748

Adrian-Viorel Diaconu

Publication date: 23 January 2019

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.00486

zbMATH Keywords

quadratic Dirichlet \(L\)-functionsWeyl group multiple Dirichlet seriesrational function fieldscubic moment

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) (zeta (s)) and (L(s, chi)) (11M06)

Related Items (7)

The mixed second moment of quadratic Dirichlet \(L\)-functions over function fields ⋮ The mean values of cubic \(L\)-functions over function fields ⋮ Secondary terms in the asymptotics of moments of \(L\)-functions ⋮ Ratios conjecture for quadratic Hecke \(L\)-functions in the Gaussian field ⋮ Moments of quadratic twists of elliptic curve \(L\)-functions over function fields ⋮ A representation theory approach to integral moments of \(L\)-functions over function fields ⋮ Moments of quadratic Dirichlet \(L\)-functions over function fields

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Conjectures for the integral moments and ratios of \(L\)-functions over function fields
• Metaplectic Whittaker functions and crystal bases
• Weyl group multiple Dirichlet series, Eisenstein series and crystal bases
• Weyl group multiple Dirichlet series constructed from quadratic characters
• Hecke modules from metaplectic ice
• Nonvanishing of quadratic Dirichlet \(L\)-functions at \(s=\frac{1}{2}\)
• The third moment of quadratic Dirichlet \(L\)-functions
• The second and third moment of \(L(1/2,\chi)\) in the hyperelliptic ensemble
• The fourth moment of quadratic Dirichlet \(L\)-functions over function fields
• On the cubic moment of quadratic Dirichlet \(L\)-functions
• A Yang-Baxter equation for metaplectic ice
• Weyl group multiple Dirichlet series. III: Eisenstein series and twisted unstable \(A_r\)
• Metaplectic covers of Kac-Moody groups and Whittaker functions
• The metaplectic Casselman-Shalika formula
• Moments of zeta functions associated to hyperelliptic curves over finite fields
• Weyl Group Multiple Dirichlet Series
• Some extremal functions in Fourier analysis. II
• On the p-parts of quadratic Weyl group multiple Dirichlet series
• Constructing Weyl group multiple Dirichlet series
• Multiple Dirichlet Series and Moments of Zeta and L-Functions
• Traces, high powers and one level density for families of curves over finite fields
• Improving the Error Term in the Mean Value of in the Hyperelliptic Ensemble
• Introduction: Multiple Dirichlet Series
• Conjectures and Experiments Concerning the Moments ofL(1/2, χ_d)
• Integral moments of L-functions
• Affine Weyl Group Multiple Dirichlet Series: Type $\tilde{A}$
• Weyl group multiple Dirichlet series for symmetrizable Kac-Moody root systems

This page was built for publication: On the third moment of \(L(\frac{1}{2}, \chi_d)\). I: The rational function field case