p-Converse to a Theorem of Gross-Zagier, Kolyvagin, and Rubin for Small Primes

Citation

Yu, Qiyao (Vivian) (2021) p-Converse to a Theorem of Gross-Zagier, Kolyvagin, and Rubin for Small Primes. Senior thesis (Major), California Institute of Technology. doi:10.7907/ccbk-ht28. https://resolver.caltech.edu/CaltechTHESIS:06022021-000654935

Abstract

Let E be a CM elliptic curve over the rationals and p a good, ordinary prime. We show the implication: corank_{(Z_p)}Sel_(p^∞)(E/_Q) = 1 ⟹ ord_(s=1)L(s,E/_Q) = 1 for the p^∞-Selmer group Sel_(p^∞)(E/_Q) and the complex L-function L(s,E/_QQ) in the case of p = 2, 3.

Item Type:

Thesis (Senior thesis (Major))

Subject Keywords:

Number Theory

Degree Grantor:

California Institute of Technology

Division:

Physics, Mathematics and Astronomy

Major Option:

Mathematics

Awards:

Eric Temple Bell Undergraduate Mathematics Research Prize, 2021. Taussky-Todd Mathematics Prize Fund, 2020.

Thesis Availability:

Public (worldwide access)

Research Advisor(s):

Burungale, Ashay

Thesis Committee:

Burungale, Ashay (chair)
Mantovan, Elena
Ramakrishnan, Dinakar

Defense Date:

4 May 2021

Record Number:

CaltechTHESIS:06022021-000654935

Persistent URL:

https://resolver.caltech.edu/CaltechTHESIS:06022021-000654935

DOI:

10.7907/ccbk-ht28

ORCID:

Author	ORCID
Yu, Qiyao (Vivian)	0000-0002-6820-4371

Default Usage Policy:

No commercial reproduction, distribution, display or performance rights in this work are provided.

ID Code:

14225

Collection:

CaltechTHESIS

Deposited By:

Qiyao Yu

Deposited On:

02 Jun 2021 21:07

Last Modified:

03 Nov 2021 20:18

Thesis Files

PDF (complete thesis) - Final Version
See Usage Policy.
359kB

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