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AuthorReck, Hans-Peterdc.contributor.author
Date of accession2016-03-15T09:04:20Zdc.date.accessioned
Available in OPARU since2016-03-15T09:04:20Zdc.date.available
Year of creation2014dc.date.created
AbstractThe study of sums that contain the Möbius- function has a long tradition as we have already indicated. The aim of this work was to estimate such sums, in which Dirichlet-characters modulo q occur as well and the sum runs only over those numbers that do not contain large prime factors. The summation could be reduced by Perron"s formula to an integral, while two mean value calculations were carried out, one over the imaginary parts and one over the Dirichlet- characters. Claudia Fischer has already used in her thesis an averaging over the imaginary parts. The averaging over the Dirichlet- characters was made because the path of integration is chosen specifically for each Dirichlet- character. Perron"s formula leads us to an integral with two parts. The first part is calculated based on the method of Baker and Harman combined with the path of integration of Maier and Montgomery as a piecewise linear contour. Here, we use monotonicity principles on horizontal lines which are parallel to the real axis and it is examined how many times the value of the inverse of the Dirichlet- L- series exceeds a certain limit. This is determined by dividing the candidate pairs of imaginary parts and characters into three sets and estimating their contribution. In the second part we use the inclusion- exclusion principle to estimate uniformly the sum contained in the integral.dc.description.abstract
Languageendc.language.iso
PublisherUniversität Ulmdc.publisher
LicenseStandarddc.rights
Link to license texthttps://oparu.uni-ulm.de/xmlui/license_v3dc.rights.uri
Dewey Decimal GroupDDC 510 / Mathematicsdc.subject.ddc
LCSHExponential sumsdc.subject.lcsh
LCSHMöbius functiondc.subject.lcsh
TitleExponentialsummen mit der Möbiusfunktiondc.title
Resource typeDissertationdc.type
DOIhttp://dx.doi.org/10.18725/OPARU-2562dc.identifier.doi
PPN782266908dc.identifier.ppn
URNhttp://nbn-resolving.de/urn:nbn:de:bsz:289-vts-88508dc.identifier.urn
GNDAnalytische Zahlentheoriedc.subject.gnd
GNDExponentialsummedc.subject.gnd
GNDMöbius-Funktiondc.subject.gnd
FacultyFakultät für Mathematik und Wirtschaftswissenschaftenuulm.affiliationGeneral
Date of activation2014-03-24T14:57:25Zuulm.freischaltungVTS
Peer reviewneinuulm.peerReview
Shelfmark print versionW: W-H 13.561uulm.shelfmark
DCMI TypeTextuulm.typeDCMI
VTS-ID8850uulm.vtsID
CategoryPublikationenuulm.category
University Bibliographyjauulm.unibibliographie


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