Functiones et Approximatio Commentarii Mathematici

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

Olivier Ramaré

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Abstract

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 $\Re s=1$. This leads to some refined bounds on $L(s,\Xi)$.

Article information

Source
Funct. Approx. Comment. Math., Volume 42, Number 2 (2010), 145-151.

Dates
First available in Project Euclid: 29 June 2010

Permanent link to this document
https://projecteuclid.org/euclid.facm/1277811637

Digital Object Identifier
doi:10.7169/facm/1277811637

Mathematical Reviews number (MathSciNet)
MR2674535

Zentralblatt MATH identifier
1205.11122

Subjects
Primary: 11R42: Zeta functions and $L$-functions of number fields [See also 11M41, 19F27] 11M06: $\zeta (s)$ and $L(s, \chi)$
Secondary: 11M20: Real zeros of $L(s, \chi)$; results on $L(1, \chi)$

Keywords
Hecke Grossencharakter Dirichlet $L$-functions

Citation

Ramaré, Olivier. Comparing $L(s,\chi)$ with its truncated Euler product and generalization. Funct. Approx. Comment. Math. 42 (2010), no. 2, 145--151. doi:10.7169/facm/1277811637. https://projecteuclid.org/euclid.facm/1277811637


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