Moments of Quadratic Hecke $L$-functions of Imaginary Quadratic Number Fields

Abstract

In this paper, we study the moments of central values of Hecke $L$-functions associated with quadratic characters in $\mathbb{Q}(i)$ and $\mathbb{Q}(\omega )$ with $\omega =exp(2\pi i/3)$ and establish some quantitative non-vanishing result for these $L$-values.

12 pages

Cited by in corpus (8)

• Moments of central values of quartic Dirichlet $L$-functions
• First moment of central values of quadratic Hecke $L$-functions in the Gaussian field
• Moments and Non-vanishing of central values of Quadratic Hecke $L$-functions in the Gaussian Field
• First Moments of Some Hecke $L$-functions of Prime Moduli
• Moments and One level density of sextic Hecke $L$-functions of $\mathbb{Q}(\omega )$
• First moment of central values of some primitive Dirichlet $L$-functions with fixed order characters
• Moments of central values of cubic Hecke $L$-functions of $\mathbb{Q}(i)$
• Moments and One level density of certain unitary families of Hecke {$L$}-functions