Comparing $L(s, \chi)$ with its truncated Euler product and generalization

Olivier Ramaré (1, 2)

1 CNRS - Centre National de la Recherche Scientifique
2 LPP - Laboratoire Paul Painlevé - UMR 8524

We show that any $L$-function attached to a non-exceptionnal Hecke Grossencharakter $\Xi$ may be approximated by a truncated Euler product when $s$ lies near the line $s = 1$. This leads to some refined bounds on $L(s, \Xi)$.

Domaines: Théorie des nombres [math.NT]

Olivier Ramaré. Comparing $L(s, \chi)$ with its truncated Euler product and generalization. Functiones et Approximatio Commentarii Mathematici, 2010, 42 (2), pp.145-151. ⟨hal-02572735⟩