The fourth moment of central values of quadratic Hecke $L$-functions in the Gaussian field

Abstract

We obtain an asymptotic formula for the fourth moment of central values of a family of quadratic Hecke $L$-functions in the Gaussian field under the generalized Riemann hypothesis (GRH). We also establish lower bounds unconditionally and upper bounds under GRH for higher moments of the same family.

31 pages

References in corpus (3)

• One level density of low-lying zeros of quadratic and quartic Hecke $L$-functions
• The fourth moment of quadratic Dirichlet $L$-functions
• Moments and Non-vanishing of central values of Quadratic Hecke $L$-functions in the Gaussian Field

Cited by in corpus (3)

• Non-vanishing of central values of quadratic Hecke $L$-functions of prime moduli in the Gaussian field
• Real zeros of quadratic Hecke $L$-functions
• One level density of low-lying zeros of quadratic Hecke $L$-functions to prime moduli