Counting elliptic curves of bounded Faltings height
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | eng |
| Published: |
Massachusetts Institute of Technology
2016
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/104589 |
| _version_ | 1826199910106529792 |
|---|---|
| author | Hortsch, Ruthi |
| author2 | Bjorn Poonen. |
| author_facet | Bjorn Poonen. Hortsch, Ruthi |
| author_sort | Hortsch, Ruthi |
| collection | MIT |
| description | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016. |
| first_indexed | 2024-09-23T11:27:44Z |
| format | Thesis |
| id | mit-1721.1/104589 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T11:27:44Z |
| publishDate | 2016 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1045892019-04-12T16:26:24Z Counting elliptic curves of bounded Faltings height Hortsch, Ruthi Bjorn Poonen. Massachusetts Institute of Technology. Department of Mathematics. Massachusetts Institute of Technology. Department of Mathematics. Mathematics. Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016. Cataloged from PDF version of thesis. Includes bibliographical references (pages 47-50). Because many invariants and properties of elliptic curves are difficult to understand directly, the study of arithmetic statistics instead looks at what happens "on average", using heights to make this notion rigorous. Previous work has primarily used the naive height, which can be calculated easily but is not defined intrinsically. We give an asymptotic formula for the number of elliptic curves over Q with bounded Faltings height. Silverman [34] has shown that the Faltings height for elliptic curves over number fields can be expressed in terms of the minimal discriminant and period of the elliptic curve. We use this to recast the problem as one of counting lattice points in an unbounded region in R2 defined by transcendental equations, and understand this region well enough to give a formula for the number of these lattice points. by Ruthi Hortsch. Ph. D. 2016-09-30T19:37:09Z 2016-09-30T19:37:09Z 2016 2016 Thesis http://hdl.handle.net/1721.1/104589 958829384 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 50 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Hortsch, Ruthi Counting elliptic curves of bounded Faltings height |
| title | Counting elliptic curves of bounded Faltings height |
| title_full | Counting elliptic curves of bounded Faltings height |
| title_fullStr | Counting elliptic curves of bounded Faltings height |
| title_full_unstemmed | Counting elliptic curves of bounded Faltings height |
| title_short | Counting elliptic curves of bounded Faltings height |
| title_sort | counting elliptic curves of bounded faltings height |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/104589 |
| work_keys_str_mv | AT hortschruthi countingellipticcurvesofboundedfaltingsheight |