The fourth moment of quadratic Dirichlet $L$-functions

Abstract

We study the fourth moment of quadratic Dirichlet $L$-functions at $s=\frac{1}{2}$. We show an asymptotic formula under the generalized Riemann hypothesis, and obtain a precise lower bound unconditionally. The proofs of these results follow closely arguments of Soundararajan and Young [19] and Soundararajan [17].

arXiv commentabstract and introduction substantially revised; typos/mistakes fixed; more detail given; accept by Math. Z

References in corpus (4)

• Conjectures for the integral moments and ratios of L-functions over function fields
• The first moment of quadratic Dirichlet L-functions
• The third moment of quadratic Dirichlet L-functions
• Lower bounds for moments of L-functions: symplectic and orthogonal examples

Cited by in corpus (6)

• Sharp upper bounds for moments of quadratic Dirichlet $L$-functions
• Non-vanishing for cubic $L$--functions
• Moments and Non-vanishing of central values of Quadratic Hecke $L$-functions in the Gaussian Field
• The fourth moment of central values of quadratic Hecke $L$-functions in the Gaussian field
• Hybrid Euler-Hadamard Product for Dirichlet $L$-functions with Prime conductors over Function Fields
• First Moments of Some Hecke $L$-functions of Prime Moduli