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master's thesis
Birch i Swinnerton-Dyerova slutnja
Zagreb: University of Zagreb, Faculty of Science, 2016. urn:nbn:hr:217:369567
Sikirić, Marko
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Sikirić, M. (2016). Birch i Swinnerton-Dyerova slutnja (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:369567

Sikirić, Marko. "Birch i Swinnerton-Dyerova slutnja." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:369567

Sikirić, Marko. "Birch i Swinnerton-Dyerova slutnja." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:369567

Sikirić, M. (2016). 'Birch i Swinnerton-Dyerova slutnja', Master's thesis, University of Zagreb, Faculty of Science, accessed 03 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:369567

Sikirić M. Birch i Swinnerton-Dyerova slutnja [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2016 [cited 2024 November 03] Available at: https://urn.nsk.hr/urn:nbn:hr:217:369567

M. Sikirić, "Birch i Swinnerton-Dyerova slutnja", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:217:369567

Metadata
TitleBirch i Swinnerton-Dyerova slutnja
AuthorMarko Sikirić
MentorFilip Najman (mentor)
Committee memberFilip Najman (predsjednik povjerenstva)
Committee memberDragutin Svrtan (član povjerenstva)
Committee memberTomislav Pejković (član povjerenstva)
Committee memberMirko Primc (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2016-09-23, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu smo probali što preciznije objasniti ovu važnu matematičku slutnju. Zbog matematičke dubine najvažniji rezultati su samo iskazani. Ono što smo pokušali vidjeti u radu je što točnija definicija glavnih pojmova i njihovo objašnjenje. Na početku rada dajemo općenitu sliku eliptičkih krivulja te njihovih osnovnih svojstava. Kasnije se trudimo da što preciznije pojasnimo pojmove L-funkcija i Tate-Šafarevičeve grupe, gdje ulazimo kratko u pojašnjenje p-adskih brojeva i Galoisove kohomologije. Na kraju dajemo iskaz Birch i Swinnerton-Dyerove slutnje, te navodimo glavne rezultate i posljedice. Svakako rad treba shvatiti kao uvod u ovo duboko područje matematike.
Abstract (english)
In this work we tried, as precise as possible, to define and explain this extraordinary conjecture. The deepest results are just stated. We tried to show, as exactly as possible, the main objects and their explanation. First we showed the main properties of elliptic curves and the mathematical theory around them. Then we define and explain L-functions and the very elusive Tate-Šafarevič group, where we to come to p-adic numbers and briefly touch on the subject of Galois Cohomology. At the end we state the Birch and Swinnerton-Dyer conjecture and try to understand where such a strong idea comes from. We show the main results and some consequences of this conjecture. This work is to be understood as an introduction to this wide and deep mathematical domain.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:369567
Study programmeTitle: Computer Science and Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-02-06 15:06:30