Moments of central values of cubic Hecke $L$-functions of $\mathbb{Q}(i)$

TL;DR

This paper investigates the average behavior of central values of cubic Hecke L-functions over (i) and proves that a positive proportion of these values do not vanish, advancing understanding of their distribution.

Contribution

It provides the first quantitative non-vanishing results for cubic Hecke L-functions in (i), using moment calculations and analytic techniques.

Findings

Established non-vanishing of a positive proportion of L-values

Computed moments of cubic Hecke L-functions in (i)

Enhanced understanding of the distribution of these L-values

Abstract

In this paper, we study moments of central values of cubic Hecke $L$-functions in $\mathbb{Q}(i)$, and establish quantitative non-vanishing result for those values.