6 papers
Local statistics and average rank of genus hyperelliptic curves with a Weierstrass point
Keunyoung Jeong, Junyeong Park
In this paper, we determine the probability that a genus hyperelliptic curve with a Weierstrass point over a number field has good reduction at a given prime of residue charact…
Arithmetic BF theory and the Cassels-Tate pairing
Jeehoon Park, Junyeong Park
We give a systematic treatment of the arithmetic BF theory, introduced by Carlson and Kim. We observe that the Cassels-Tate pairing can be naturally interpreted as an arithmetic BF…
Goldfeld conjecture for non-hyperelliptic direction
Keunyoung Jeong, Junyeong Park
Since the curve has a large automorphism group, there exist twist families arising from non-hyperelliptic directions. In this paper, we give an explicit upper bound o…
The average analytic rank of elliptic curves with prescribed level structure
Peter J. Cho, Keunyoung Jeong, Junyeong Park
Assuming the Hasse--Weil conjecture and the generalized Riemann hypothesis for the -functions of the elliptic curve, we give an upper bound of the average analytic rank of ellip…
Nonvanishing of -function of some Hecke characters on cyclotomic fields
Keunyoung Jeong, Yeong-Wook Kwon, Junyeong Park
In this paper, we show the nonvanishing of some Hecke characters on cyclotomic fields. The main ingredient of this paper is a computation of eigenfunctions and the action of Weil r…
On the Jacobian of hyperelliptic curves
Keunyoung Jeong, Junyeong Park, Donggeon Yhee
In this paper, we study the algebraic rank and the analytic rank of the Jacobian of hyperelliptic curves for integers . Namely, we first provide a condition on…