arXiv subjects

Donggeon Yhee

Publications and source records attributed to Donggeon Yhee.

2 recordsLinked to original sources

arXiv2021

On the Jacobian of hyperelliptic curves $y^2 = x^5 + m^2$

In this paper, we study the algebraic rank and the analytic rank of the Jacobian of hyperelliptic curves $y^2 = x^5 + m^2$ for integers $m$. Namely, we first provide a condition on $m$ that gives a bound of the size of Selmer group and then we provide a condition on $m$ that makes $L$-functions non-vanishing. As a consequence, we construct a Jacobian that satisfies the rank part of the Birch--Swinnerton-Dyer conjecture.

math.NT↗

arXiv2015

On a conjecture of Gross and Zagier

Gross and Zagier conjectured that if the analytic rank of a rational elliptic curve is 1, then the order of the rational torsion subgroup of the elliptic curve divides the product of Tamagawa number, Manin constant, and the square root of the order of Tate--Shafarevich group over an imaginary quadratic field. In this paper, we show that this conjecture is true.

math.NT↗