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
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 K∈Cl such that the difference rK(E)−rQ(E) between analytic rank is less than a for a≍l. This result gives conjectural evidence that the Diophantine Stability problem suggested by Mazur and Rubin holds for most of K∈Cl.