Zur Kurzanzeige

2004-09-06Buch DOI: 10.18452/2591
On Artin's L-funcions. II: Dirichlet Coefficients
dc.contributor.authorNicolae, Florin
dc.date.accessioned2017-06-15T17:39:23Z
dc.date.available2017-06-15T17:39:23Z
dc.date.created2005-11-03
dc.date.issued2004-09-06none
dc.identifier.urihttp://edoc.hu-berlin.de/18452/3243
dc.description.abstractLet $K/\Q$ 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.isoeng
dc.publisherHumboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
dc.relation.ispartofseriesPreprints aus dem Institut für Mathematik - 19, Mathematik-Preprints, ISSN:0863-0976
dc.subjectZeta functions and $L$-functions of number fieldseng
dc.subject.ddc510 Mathematik
dc.titleOn Artin's L-funcions. II: Dirichlet Coefficients
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-10052253
dc.identifier.doihttp://dx.doi.org/10.18452/2591
local.edoc.container-titlePreprints aus dem Institut für Mathematik
local.edoc.container-titleMathematik-Preprints
local.edoc.container-issn0863-0976
local.edoc.pages6
local.z-edoc.journal-periodikumAusgabe19,
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-volume2004
local.edoc.container-issue19
local.edoc.container-year2004
local.edoc.container-erstkatid2075199-0

Zur Kurzanzeige