3 citations · 3 across the 10 of their papers we have counts for
10 papers · 1 filter
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…
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…
On the distribution of analytic ranks of elliptic curves
Peter J. Cho, Keunyoung Jeong
In this paper, under GRH for elliptic -functions, we give an upper bound for the probability for an elliptic curve with analytic rank for , and also give an…
Distribution of root numbers of Hecke characters attached to some elliptic curves
Keunyoung Jeong, Jigu Kim, Taekyung Kim
In this paper, we show that an action on the set of elliptic curves with j= 1728 preserves a certain kind of symmetry on the local root number of Hecke characters attached to such…
Counting the number of the twists of certain polarized abelian varieties
WonTae Hwang, Keunyoung Jeong
We count the number of isomorphism classes of degree -twists of some polarized abelian varieties over finite fields of odd prime dimension. This can be seen as a higher dimensio…
Infinitely many elliptic curves of rank exactly two, II
Keunyoung Jeong
In this paper, we construct an infinite family of elliptic curves whose rank is exactly two and the torsion subgroup is a cyclic group of order two or three, under the parity conje…
The exceptional set in a generalized Goldbach`s problem
Dongho Byeon, Keunyoung Jeong
In this paper, we compute the size of the exceptional set in a generalized Goldbach problem and show that for a given polynomial with a positive leading co…