Extreme central values of quadratic Dirichlet $L$-functions with prime conductors

TL;DR

This paper establishes a lower bound for the extremely large values of quadratic Dirichlet L-functions at 1/2 for prime conductors congruent to 1 mod 8, advancing understanding of their extreme behavior.

Contribution

It provides a new lower bound result for large values of quadratic Dirichlet L-functions at the critical point for a specific class of prime conductors.

Findings

Proves a lower bound for large L-values at 1/2 for primes p ≡ 1 mod 8.

Enhances understanding of the distribution of extreme values of quadratic Dirichlet L-functions.

Focuses on primes with specific congruence conditions, contributing to analytic number theory.

Abstract

In this paper we prove a lower bound result for extremely large values of $L(\frac{1}{2},\chi_p)$ with prime numbers $p\equiv 1\pmod 8$.