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Discriminants of cubic curves and determinantal representations
Manh Hung Tran
The discriminant of a smooth plane cubic curve over the complex numbers can be written as a product of theta functions. This provides an important connection between algebraic and…
Invariants of models of genus one curves and modular forms
Manh Hung Tran
An invariant of a model of genus one curve is a polynomial in the coefficients of the model that is stable under certain linear transformations. The classical example of an invaria…
Uniform bounds for rational points on complete intersections of two quadric surfaces
Manh Hung Tran
We give uniform upper bounds for the number of rational points of height at most on non-singular complete intersections of two quadrics in defined over $\mathbb{…
Counting rational points on smooth cubic curves
Manh Hung Tran
We use a global version of Heath-Brown's adic determinant method developed by Salberger to give upper bounds for the number of rational points of height at most on non-sing…