Real zeros of quadratic Hecke $L$-functions

TL;DR

This paper investigates the distribution of real zeros in quadratic Hecke L-functions over the Gaussian field, revealing that over twenty percent of these functions lack zeros in the interval (0, 1].

Contribution

It provides new results on the proportion of quadratic Hecke L-functions with no zeros in (0, 1], advancing understanding of their zero distribution.

Findings

Over twenty percent of the studied L-functions have no zeros in (0, 1]

The paper advances knowledge on the zero distribution of quadratic Hecke L-functions

It focuses on the Gaussian field case for quadratic Hecke L-functions

Abstract

We study real zeros of a family of quadratic Hecke $L$-functions in the Gaussian field to show that more than twenty percent of the members have no zeros on the interval $(0, 1]$.