Zero-Density Theorems for Families of Dirichlet $L$-functions

TL;DR

This paper establishes zero density theorems for families of Dirichlet L-functions linked to characters with moduli in sparse sets and fixed orders, advancing understanding of their zeros.

Contribution

It introduces new zero density results for Dirichlet L-functions associated with specific sparse moduli and fixed character orders, expanding existing analytic number theory techniques.

Findings

Zero density theorems for Dirichlet L-functions with sparse moduli

Results applicable to fixed order characters

Enhanced bounds on zeros in specified families

Abstract

In this paper, we prove some zero density theorems for certain families of Dirichlet $L$-functions. More specifically, the subjects of our interest are the collections of Dirichlet $L$-functions associated with characters to moduli from certain sparse sets and of certain fixed orders.