Two dimensional value-distribution of cubic Hecke $L$-functions

TL;DR

This paper studies the joint distribution of the logarithm and its derivative of cubic Hecke $L$-functions, providing asymptotic results and key decay estimates for their characteristic functions.

Contribution

It introduces the first two-dimensional asymptotic distribution results for cubic Hecke $L$-functions and develops exponential decay estimates for their characteristic functions.

Findings

Established two-dimensional asymptotic distributions.

Derived exponential decay estimates for characteristic functions.

Enhanced understanding of the distributional properties of cubic Hecke $L$-functions.

Abstract

We establish the two-dimensional asymptotic distributions of the logarithm and logarithmic derivative of $L$-functions associated with a family of cubic Hecke characters. A crucial ingredient in the proof of our main result is an exponential decay estimate for the characteristic functions of the distributions.