Show simple item record

Bernoulli numbers and regular primes
dc.contributor.advisorKala, Vítězslav
dc.creatorLe, Anh Dung
dc.date.accessioned2017-09-26T08:48:36Z
dc.date.available2017-09-26T08:48:36Z
dc.date.issued2017
dc.identifier.urihttp://hdl.handle.net/20.500.11956/90322
dc.description.abstractThe aim of this work is to study the relation between regular primes and regular Bernoulli numbers (or just simply Bernoulli numbers). By the class number formula we connect the class number to the values of Dirichlet L-series. We then compute certain values of Dirichlet L-series in terms of generalized Bernoulli numbers. In order to investigate the relations between two types of Bernoulli numbers we define the p-adic Dirichlet L-series. In the end we get a congruence between the class number and Bernoulli numbers modulo p. Since the regular primes are those which divide the corresponding class numbers this is precisely our goal. 1en_US
dc.description.abstractCı'lem pra'ce je studium vztahu mezi regula'nı'mi prvocˇı'sly a regula'rnı'mi Bernoulliho cˇı'sly (nebo jednodusě jen Bernoulliho cˇı'sly). Formulı' trˇı'dove'ho cˇı'sla spojı'me trˇı'dove' cˇı'slo s hodnotami Di- richletovy'ch L-rˇad. Pote' vypocťeme urcˇite' hodnoty Dirichletovy'ch L-rˇad pomocı' zobecneňy'ch Bernoulliho cˇı'sel. Abychom vysětrˇili vztahy mezi dveˇma typy Bernoulliho cˇı'sel, definujeme p- adicke' Dirichletovy L-rˇady. Na konci pra'ce dostaneme kongruenci mezi trˇı'dovy'm cˇı'slem a Ber- noulliho cˇı'sly modulo p. Z definice jsou regula'rnı' cˇı'sla pra'veˇ ta, ktera' deľı' prˇı'slusňa' trˇı'dova' cˇı'sla, a proto jsme dosa'hli sve'ho cı'le. 1cs_CZ
dc.languageČeštinacs_CZ
dc.language.isocs_CZ
dc.publisherUniverzita Karlova, Matematicko-fyzikální fakultacs_CZ
dc.subjectBernoulli numberen_US
dc.subjectregular primeen_US
dc.subjectideal class groupen_US
dc.subjectcyclotomic fielden_US
dc.subjectBernoulliho číslocs_CZ
dc.subjectregulární prvočíslocs_CZ
dc.subjectgrupa tříd ideálůcs_CZ
dc.subjectcyklotomické tělesocs_CZ
dc.titleBernoulliho čísla a regulární prvočíslacs_CZ
dc.typebakalářská prácecs_CZ
dcterms.created2017
dcterms.dateAccepted2017-09-05
dc.description.departmentDepartment of Algebraen_US
dc.description.departmentKatedra algebrycs_CZ
dc.description.facultyFaculty of Mathematics and Physicsen_US
dc.description.facultyMatematicko-fyzikální fakultacs_CZ
dc.identifier.repId187582
dc.title.translatedBernoulli numbers and regular primesen_US
dc.contributor.refereeVávra, Tomáš
thesis.degree.nameBc.
thesis.degree.levelbakalářskécs_CZ
thesis.degree.disciplineGeneral Mathematicsen_US
thesis.degree.disciplineObecná matematikacs_CZ
thesis.degree.programMatematikacs_CZ
thesis.degree.programMathematicsen_US
uk.thesis.typebakalářská prácecs_CZ
uk.taxonomy.organization-csMatematicko-fyzikální fakulta::Katedra algebrycs_CZ
uk.taxonomy.organization-enFaculty of Mathematics and Physics::Department of Algebraen_US
uk.faculty-name.csMatematicko-fyzikální fakultacs_CZ
uk.faculty-name.enFaculty of Mathematics and Physicsen_US
uk.faculty-abbr.csMFFcs_CZ
uk.degree-discipline.csObecná matematikacs_CZ
uk.degree-discipline.enGeneral Mathematicsen_US
uk.degree-program.csMatematikacs_CZ
uk.degree-program.enMathematicsen_US
thesis.grade.csVýborněcs_CZ
thesis.grade.enExcellenten_US
uk.abstract.csCı'lem pra'ce je studium vztahu mezi regula'nı'mi prvocˇı'sly a regula'rnı'mi Bernoulliho cˇı'sly (nebo jednodusě jen Bernoulliho cˇı'sly). Formulı' trˇı'dove'ho cˇı'sla spojı'me trˇı'dove' cˇı'slo s hodnotami Di- richletovy'ch L-rˇad. Pote' vypocťeme urcˇite' hodnoty Dirichletovy'ch L-rˇad pomocı' zobecneňy'ch Bernoulliho cˇı'sel. Abychom vysětrˇili vztahy mezi dveˇma typy Bernoulliho cˇı'sel, definujeme p- adicke' Dirichletovy L-rˇady. Na konci pra'ce dostaneme kongruenci mezi trˇı'dovy'm cˇı'slem a Ber- noulliho cˇı'sly modulo p. Z definice jsou regula'rnı' cˇı'sla pra'veˇ ta, ktera' deľı' prˇı'slusňa' trˇı'dova' cˇı'sla, a proto jsme dosa'hli sve'ho cı'le. 1cs_CZ
uk.abstract.enThe aim of this work is to study the relation between regular primes and regular Bernoulli numbers (or just simply Bernoulli numbers). By the class number formula we connect the class number to the values of Dirichlet L-series. We then compute certain values of Dirichlet L-series in terms of generalized Bernoulli numbers. In order to investigate the relations between two types of Bernoulli numbers we define the p-adic Dirichlet L-series. In the end we get a congruence between the class number and Bernoulli numbers modulo p. Since the regular primes are those which divide the corresponding class numbers this is precisely our goal. 1en_US
uk.file-availabilityV
uk.publication.placePrahacs_CZ
uk.grantorUniverzita Karlova, Matematicko-fyzikální fakulta, Katedra algebrycs_CZ


Files in this item

Thumbnail
Thumbnail
Thumbnail
Thumbnail
Thumbnail
Thumbnail

This item appears in the following Collection(s)

Show simple item record


© 2017 Univerzita Karlova, Ústřední knihovna, Ovocný trh 560/5, 116 36 Praha 1; email: admin-repozitar [at] cuni.cz

Za dodržení všech ustanovení autorského zákona jsou zodpovědné jednotlivé složky Univerzity Karlovy. / Each constituent part of Charles University is responsible for adherence to all provisions of the copyright law.

Upozornění / Notice: Získané informace nemohou být použity k výdělečným účelům nebo vydávány za studijní, vědeckou nebo jinou tvůrčí činnost jiné osoby než autora. / Any retrieved information shall not be used for any commercial purposes or claimed as results of studying, scientific or any other creative activities of any person other than the author.

DSpace software copyright © 2002-2015  DuraSpace
Theme by 
@mire NV