Chang Heon Kim

On the Torsion of Elliptic Curves Over Quartic Number Fields

We determine which groups

Borcherds products associated with certain Thompson series

{\mathbb{Z}}/M{\mathbb{Z}}\oplus{\mathbb{Z}}/N{\mathbb{Z}}

Families of elliptic curves over quartic number fields with prescribed torsion subgroups

occur infinitely often as torsion groups

On the arithmetic of certain modular curves

E(K)_{\operatorname{tors}}

Mock modular period functions and L -functions of cusp forms in higher level cases

when

Rank-one quadratic twists of an infinite family of elliptic curves

K

ARITHMETIC PROPERTIES OF TRACES OF SINGULAR MODULI ON CONGRUENCE SUBGROUPS

varies over all quartic number fields and

Generators of function fields of the modular curves ₁(5) and ₁(6)

E

Normalizers of intermediate congruence subgroups of the Hecke subgroups

varies over all elliptic curves over

Linear relations between modular forms for Г0+(p)

K