2004-09-06Buch DOI: 10.18452/2591
On Artin's L-funcions. II: Dirichlet Coefficients
 dc.contributor.author Nicolae, Florin dc.date.accessioned 2017-06-15T17:39:23Z dc.date.available 2017-06-15T17:39:23Z dc.date.created 2005-11-03 dc.date.issued 2004-09-06 none dc.identifier.uri http://edoc.hu-berlin.de/18452/3243 dc.description.abstract Let $K/\Q$ be a finite Galois extension, let $\chi$ be a character of the Galois group $G=\Gal(K/\Q)$ which does not contain the principal character, let $L_{ur}(s,\chi,K/\Q)$ be the unramified part of the corresponding Artin $L$-function, and let $$L_{ur}(s,\chi,K/\Q)^\frac{1}{\chi(1)}=\sum_{n=1}^\infty\frac{a_n}{n^s}$$ for $\Re(s)>1$. Then:\\ (i) The coefficients $a_n$ are algebraic numbers of the field $\Q(e^\frac{2\pi i}{|G|})$ and $|a_n|\leq 1$ for every $n\geq 1$ ;\\ (ii) The summatory function $\sum_{n\leq x}a_n$ is ${\bf o}(x)$ as $x\rightarrow\infty$. eng dc.language.iso eng dc.publisher Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik dc.relation.ispartofseries Preprints aus dem Institut für Mathematik - 19, Mathematik-Preprints, ISSN:0863-0976 dc.subject Zeta functions and $L$-functions of number fields eng dc.subject.ddc 510 Mathematik dc.title On Artin's L-funcions. II: Dirichlet Coefficients dc.type book dc.identifier.urn urn:nbn:de:kobv:11-10052253 dc.identifier.doi http://dx.doi.org/10.18452/2591 local.edoc.container-title Preprints aus dem Institut für Mathematik local.edoc.container-title Mathematik-Preprints local.edoc.container-issn 0863-0976 local.edoc.pages 6 local.z-edoc.journal-periodikum Ausgabe19, local.edoc.type-name Buch local.edoc.container-type series local.edoc.container-type-name Schriftenreihe local.edoc.container-volume 2004 local.edoc.container-issue 19 local.edoc.container-year 2004 local.edoc.container-erstkatid 2075199-0