Luhao Yan

On the asymptotic formula of L'(1, χ)

Let $χ$ be a quadratic Dirichlet character. In some literatures, various asymptotic formulae of $L'(1,χ)$, under the assumption that $L(1,χ)$ takes a small value, were derived. In this paper, we will give a new treatment unified for the odd and even cases, not depending on Kronecker limit formula. For imaginary quadratic fields, our result coincides with Proposition 22.10 in [1].