# Explicit bounds on exceptional zeroes of Dirichlet L-function II

## TL;DR

This paper refines bounds on exceptional zeroes of Dirichlet L-functions for even characters by improving explicit estimates and leveraging average character results with computational support.

## Contribution

It provides new explicit bounds on exceptional zeroes of Dirichlet L-functions for even characters, enhancing previous estimates through refined analysis and computational methods.

## Key findings

- Improved upper bounds for exceptional zeroes.
- Enhanced explicit estimates for $L'(\sigma;\chi)$ near $\sigma=1$.
- Utilized average character results and computational techniques.

## Abstract

This paper improves the upper bound for the exceptional zeroes of Dirichlet L-functions with even characters. The result is obtained by improving on explicit estimate for $L'(\sigma;\chi)$ for $\sigma$ close to unity, using a result on the average of Dirichlet characters, and on the lower bound for $L(1;\chi)$, with computational aid.