Uniform effective estimates for $|L(1,\chi )|$

Abstract

Let $L(s,\chi )$ be the Dirichlet $L$-function associated to a non-principal primitive Dirichlet character $\chi$ defined modulo $q$, where $q\ge 3$. We prove, under the assumption of the Generalised Riemann Hypothesis, the validity of estimates given by Lamzouri, Li, and Soundararajan on $|L(1,\chi )|$. As a corollary, we have that similar estimates hold for the class number of the imaginary quadratic field $\mathbb{Q}(\sqrt{-q})$, $q\ge 5$.

References in corpus (1)

• Numerical verification of Littlewood's bounds for $|L(1,\chi )|$

Cited by in corpus (2)

• Conditional estimates for the logarithmic derivative of Dirichlet $L$-functions
• Computing the endomorphism ring of an elliptic curve over a number field