Number Theory Seminar
in Northeast Seoul
organized by Dohoon Choi and Subong Lim
organized by Dohoon Choi and Subong Lim
Goldfeld conjecture for genus 2 curves
Keunyoung Jeong (Chonnam National University)
April 10 (Fri) 2026, 11:00 ~ 12:00
Asan science building 525
Abstract: Goldfeld's conjecture predicts that the average rank in the family of quadratic twists of an elliptic curve over the rationals is 1/2. Naive analogues of Goldfeld's conjecture have also been studied for elliptic curves over number fields and for genus 2 curves, together with the phenomenon of disparity. However, these analogues have mainly been considered in the setting of hyperelliptic twists. In this talk, we investigate a non-hyperelliptic analogue of Goldfeld's conjecture for a genus 2 curve.