A purely analytical lower bound for $L(1, \chi)$

Olivier Ramaré (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

We give a simple proof of $L(1, \chi) \sqrt{q}\gg 2^{\omega(q)}$ when $\chi$ is an odd primitive quadratic Dirichlet character of conductor $q$. In particular we do not use the Dirichlet class-number formula.

Domaines: Théorie des nombres [math.NT]

Olivier Ramaré. A purely analytical lower bound for $L(1, \chi)$. Annales Mathématiques Blaise Pascal, 2009, 16 (2), pp.259-265. ⟨10.5802/ambp.265⟩. ⟨hal-02572760⟩