On Computing the Tate Shafarevich group order and type of some rational elliptic curves of conductor less than a million.

Simple item page
dc.contributor.advisorStein, William A
dc.contributor.authorZelaya Eufemia, Gerardo E
dc.date.accessioned2019-08-14T22:36:17Z
dc.date.issued2019-08-14
dc.date.submitted2019
dc.descriptionThesis (Ph.D.)--University of Washington, 2019
dc.description.abstractIn this dissertation, I will present the tabulation of the Tate Shafarevich group order and type of around 4.5 million rational elliptic curves of conductor less than a million. These curves were obtained from the database of Cremona and that of Stein and Watkins, and I assumed standard conjectures including the Birch and Swinnerton-Dyer standard and $p$-adic conjectures and the Generalized Riemann Hypothesis. I also predict how far we are from witnessing Delaunay's asymptotic proportions on the order valuations and ranks of their Tate Shafarevich groups.
dc.embargo.lift2020-08-13T22:36:17Z
dc.embargo.termsRestrict to UW for 1 year -- then make Open Access
dc.format.mimetypeapplication/pdf
dc.identifier.otherZelayaEufemia_washington_0250E_20183.pdf
dc.identifier.urihttp://hdl.handle.net/1773/44371
dc.language.isoen_US
dc.rightsnone
dc.subjectNumber Theory
dc.subjectRational Elliptic Curves
dc.subjectTate Shafarevich group
dc.subjectMathematics
dc.subjectPhysical education
dc.subject.otherMathematics
dc.titleOn Computing the Tate Shafarevich group order and type of some rational elliptic curves of conductor less than a million.
dc.typeThesis

Files

Original bundle

Now showing 1 - 1 of 1
Thumbnail Image
Name:
ZelayaEufemia_washington_0250E_20183.pdf
Size:
802.38 KB
Format:
Adobe Portable Document Format
Download

Collections

Mathematics