The distribution of analytic ranks of elliptic curve over prime cyclic number fields

Speaker: Gyeongwon Oh

Date: Mon, Jun 17, 2024

Location: PIMS, University of British Columbia

Conference: Comparative Prime Number Theory

Subject: Mathematics, Number Theory

Class: Scientific

CRG: L-Functions in Analytic Number Theory

Abstract:

Let E be an elliptic curve over Q and Cl be the family of prime cyclic extensions of degree l over Q. Under GRH for elliptic L-functions, we give a lower bound for the probability for KCl such that the difference rK(E)rQ(E) between analytic rank is less than a for al. This result gives conjectural evidence that the Diophantine Stability problem suggested by Mazur and Rubin holds for most of KCl.