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


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.


Let E be a CM elliptic curve over the rationals and p a good, ordinary prime. We show the implication: corank(Zp)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:
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
Deposited By: Qiyao Yu
Deposited On:02 Jun 2021 21:07
Last Modified:03 Nov 2021 20:18

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