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

Abstract

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

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References in corpus (6)

• Bounds for moments of quadratic Dirichlet $L$-functions of prime-related moduli
• Determination of $\text{GL}(3)$ cusp forms by central values of quadratic twisted $L$-functions
• Extreme central $L$-values of almost prime quadratic twists of elliptic curves
• Lower bounds for moments of quadratic twists of modular $L$-functions
• Twisted first moment of quadratic and quadratic twist $L$-functions
• Lower bounds for moments of quadratic twisted self-dual $\text{GL}(3)$ central $L$-values